Sony a7iii. Camera format set to just RAW. Lightroom only showing JPEG version of img and never RAW

The Windows Photos app cannot display raw files, so it displays the jpg embedded in the raw file.

Your screenshot shows that you do have a raw file open in LrC.

Profile is set to Adobe Color, which is only for raw files. If this was a jpg, it would just be "Color".

Also, Temp is set to 3500 (Kelvin), another indication of a raw file. For a jpg, the scale would go from -100 to +100.

If you select this file in Library, the Metadata panel will most likely display 154.arw under File Name.

The jpg has been rendered in the camera, based on the current camera settings. You seem to be using a setting that underexposes the image to prevent highlights from blowing out. You can probably recover the highlight detail in the raw file by using the Highlights slider.

LrC creates its own rendering of the raw file, and ignores the camera settings.

There is nothing wrong. Your screenshot shows Lightroom is editing a raw photo, not a jpeg photo. You can see that if you look at the white balance setting options. You see the Temperature is set in Kelvin. That is indicative for raw. Jpeg has white balance already 'baked in', so you would see only correction options, both initially set to zero.

I've uploaded all of my pictures to my pc (uploaded as .arw files) and upon viewing them on the default photo application for windows 10, it shows a 'filtered' preview (jpeg) of the image for a few seconds before switching to the raw version (dulled out version, no filters, etc).

My issue is when uploading my pictures to Lightroom, Lightroom only shows the jpeg images for me to edit and never the raw. I get this same issue when uploading my pictures to photoshop too.

Do you mean import?

This is what happens when you import a RAW. Initially, you see the JPG preview embedded in the RAW files. Then a few seconds later Lightroom Classic renders its own version of the RAW and the appearance of the image changes. This is normal, and cannot be turned off.

You can create presets to be applied at Import such that the first rendered image of your RAWs is more to your liking initially.

(When you write of 'uploading my pictures to Lightroom', I will assume this means importing your pictures into the Lightroom Classic Catalog - though the basic issue is AFAICT the same across both Lightroom, and Lightroom Classic.)

If your camera is set to shoot Raw only then there is no JPG file being saved or imported. Therefore what you are importing is indeed a Raw. This is confirmed in your screenshot - file type ".ARW".  Even if your camera was set to shoot Raw+JPG, and even if your image reports as Raw+JPG inside the Catalog, this would still only be processing from a Raw image. Only when you see a separate image with the file type reported as JPG only, are you actually dealing with a JPG.

That said, when the camera shoots a Raw it includes a JPG preview and this reflects whatever image settings were active in the camera menu at the time of shooting. So that preview will itself look very similar to what the camera would have otherwise produced, if it had been set to JPG instead of to Raw.

Also, a record of these in-camera image settings is included in the Raw. To the extent that these settings are compatibly usable, LrC may employ equivalents in response or else it may be set to use certain settings regardless, for its own initial processing default - controlling what you will therefore see before you commence your own editing. 

Thus, there is no single standard appearance that all Raws will always show. If you are viewing a Raw you are either still seeing the embedded preview from the camera, or else the results of one or another Raw conversion. And the particular conversion that you will initially see is to some extent within your control but also can be specific to the viewing application and also how well or badly it understands any metadata attached to the file. A Raw conversion utility supplied by the camera manufacturer will read and use the camera settings present exactly the same as the camera would have done. Windows photos viewer does not possess that level of camera specific support. 

If the presentation you are used to seeing with Raws at import has always been dull up to now, then that might become your familiar way to recognise what is or is not a Raw. But this is not necessarily so. Consider: after you've applied your own editing choices the appearance will presumably never be dull, but the underlying file will still equally be a Raw then.