Setting up a Motif XS to work with a DAW is complex but straight forward as long as you follow all the steps. It will work with all of the DAWs you’ve mentioned... including FL; It has special Remote Control Surface templates for interfacing with Cubase and Logic Pro.
What you need (that you have not mentioned) I will try to mention below — if you do not mention it, we will assume you have not done it); and it is part of the cause. Use this as a checklist:

Download and install:
__ “USB-MIDI Driver v3.1.4 for Windows” (required)
__ “Motif XS Extension 1.6.1 for Win” (required)
__ “Motif XS Editor Standalone/VST v1.6.4 for Win (optional)

The USB-MIDI Driver allows you to communicate MIDI between your Yamaha keyboard and your Windows computer. This should work immediately - MIDI communication is fairly automatic and gives you very little trouble. (It does not handle Audio).
The Motif XS Extension is a bit of code written by Yamaha that teaches Cubase specifics about your Yamaha Motif XS… It will allow you see and address the Ports by their proper names (useful when you’re using 16-in/6-out FireWire buses) and it should configure your MIDI IN Port options properly.
You can fix what it sets up as follows…

On the screen shot you linked to: the “MIDI PORT SETUP” screen
In the column named “In ‘All MIDI Inputs’” — all four Motif XS Port options should NOT be checked (this will create problems- specifically, front panel buttons playing sounds) you do not want to merge all of these ports — you want only ports that you want to interact with your Midi Tracks. The Motif XS uses Port 1 for musical uses: notes, tempos, controllers, etc.
Make the following corrections:

”In ‘All MIDI Inputs’” — This column informs Cubase which connected MIDI Ports are going to be considered an active Input device (typically: what keyboard do you want to use to play) to write MIDI Data to your MIDI Tracks. You incorrectly have all four Port checked.
Port 1 should be marked… it is your Motif XS keyboard/controllers
Port 2 should NOT be marked here… it is setup separately, elsewhere, when using the XS as a Remote Control Surface to remote control (start/stop, play/rec, select and arm tracks, etc., etc) on your DAW. Uncheck this box.
Port 3 should be marked if you want to connect a second external device to the XS’s 5-pin MIDI IN and OUTs. For example, say you have another MIDI synth that you want to use as a controller… connect it here, it will show up as “Motif XS-3” (Port3) - meaning you can play both keyboards simultaneously. The Motif XS is “Motif XS-1” and your other synth is “Motif XS-3”.
Port 4 should be marked if you wish to connect the “Motif XS VST Editor”. Port 4 allows direct 1:1 communication between the “VST Editor’s” graphic user interface and the XS hardware front panel.

The Motif XS Editor Standalone VST when used with a VST3 compatible DAW, like Cubase AI, you can setup to use your Motif XS as a VST — meaning you can take advantage of Advanced Integration (AI) -special audio routing- which lets process your Motif XS with VST plugin Effects… same as you would VSTi’s!
It allows you to return audio to Cubase via advanced routing, process it with VST effects, etc., and to use the FREEZE audio, and the EXPORT > AUDIO MIXDOWN features — while your tracks remain MIDI. The advantage is being able to continue to manipulate your data as MIDI, before committing to Audio. (These are some of the features you can use, you do not have to… but the reasons to at least try Cubase become obvious, rather quickly). In order to get this working you must setup your Audio. It VST (Virtual Studio Technology) requires both MIDI and Audio to be working together…

Once MIDI connections are properly made you should be able to move to routing Audio. Sending audio to the computer is a separate setup. MIDI is not sound. MIDI is coded messages. The coded messages can be documented (recorded) to a MIDI Track — where they can be easily edited/corrected/replaced, etc. If the coded messages are captured and routed back to the source (XS) the XS’s Tone Generator will create sound. But MIDI is not sound…

Documenting (recording) that sound to Audio Tracks in your computer requires a different Driver, a different routing, and more gear (audio interface/monitor speakers).

Audio Recording requires selecting an Audio Interface and it’s ASIO Driver
In order to hear audio through your DAW you need to have an Audio Interface and a pair of Monitor Speakers connected to that Audio Interface. Audio generates mountains of data, while MIDI data is tiny by comparison. Audio Streaming Input Output or ASIO is a protocol for the high speed transfer needed to play and record music simultaneously. Without a special high speed (low latency, is the term you’ll hear) driver, it becomes untenable. The typical built-in drivers can record, sure; and they can playback, no problem… what they have trouble with is recording while playing back. It’s call “overdubbing” — the most important thing you need a computer to do for you when your a one-person operation!

The job of the audio interface is to convert analog signal (like the XS) to your computer (you’ll connect the Main L&R Outputs of the Motif XS to a pair of inputs on the audio interface __ the interface will connect to the computer via USB or FireWire. Audio Interface devices will typically have a recommended Driver. The “driver” is designed and tested for the particular brand/model audio interface. (It’s the specification the manufacturer is expecting you to get) — recommended to seek out the proper driver for your specific Audio Interface.

FYI: The Motif XS can act as an audio interface via FW (FireWire) requires an FW16E and a computer capable of FW. You don’t mention FW so we’ll leave this out… FW has seen its heyday 2003-2013… you’ll find it difficult/if not impossible to run and get support for FW on current computers and laptops
You can, of course, connect the XS’s analog outputs to any appropriate external USB audio interface

The Audio Interface is also responsible for converting digital audio to analog outputs (like a connected pair of Monitor Speaker). The device acting as the audio interface must be used to send signal to your speakers. This means a separate set of speakers from those that come with your computer.

Q — What are you using for your Audio Interface?
You will need to install its ASIO Driver and select that Driver for the Audio System in your DAW
Q — What type of connectors are on your audio interface? (you need two channels, a L/R to be able to record stereo).

Let us know. We cannot really go forward without knowing the next bit of hardware (audio interface, monitor speakers). Headphones can be used in place of monitor speakers but the must be connected to the audio interface!

There is key input appearing so the software has picked up the Motif and is connected but there is still no sound or any notes or patterns being recorded when I click record.

Boiling down the key takeaways:

The Motif XS USB connection does not deliver audio. It's used for MIDI and other housekeeping.

To get Audio to your computer you either need to use FireWire or a dedicated audio interface while connecting this audio interface's analog audio inputs to Motif XS's analog audio outputs. Then the DAW would configure this non-Motif-XS audio interface as the audio device.

FireWire is very unlikely because it requires both a FireWire expansion board in your XS and also that your computer (including drivers) has full support for FireWire which "no" modern computers natively support.

I'm ignoring the MIDI port topic here not that it isn't important. Only because that work is not needed to start getting XS's audio into your DAW.