Can't Set Profile Immediately After Switching to Develop Module

I can't replicate the issue and don't recall seeing it in the past. I have the profile set using the new Raw Defaults feature in Preferences> Presets with a separate develop preset for each camera model. Previously I had that implemented uisng the Default Settings update for each camera model. You may find that helpful.

https://helpx.adobe.com/in/lightroom-classic/help/raw-defaults.html

This bug has bugged me for years. Never bothered me enough to complain about it but I know exactly what you mean. This happens on every single Lightroom Classic installation I have seen (I teach classes and I often try this on students' computers (both macs and pcs) and invariably this happens). You switch into develop and if you try to change the profile too quickly (i.e. the first thing you do), the change won't stick. If you wait a few seconds (I am not very patient) until the image has loaded, the chnage will stick. This happens on fresh installs on completely new computers, on empty catalog that you just imported into and after resetting preferences. You really only see this if you immediately almost while switching hit the popup so I just take it as a sign that I need to slow down (Lightroom Classic often tells me this 😉 )

RE: profile on import - because I shoot multiple camera brands, I don't set profile on Import since some of the profiles only work on certain cameras' images.

Actually, consider a different approach, in preferences edit the settings for importing RAW images, change to camera specific, select a user create preset pointing to the Camera matching profile (folks, how is that part accomplished?)

https://helpx.adobe.com/lightroom-classic/help/raw-defaults.html 

https://www.youtube.com/watch?v=XGCnR9qEqA4 

Not sure how to make a profile a "favorite"

By default, the Camera Matching Profiles are not Favorites, and they are not readily available with one click as yours are. By default I need to browse, to get to them.

As to adding as a favorite, when browsing them, muse hover over the profile tile, and Add to Favorite will appear

One more step to try is to create a new catalog, import some image files, and see if the issue remains. If so use the Creative Cloud app to uninstall LrC, restart your system and then reinstall LrC 10.3. Nothing will be lost, but you may need to reassociate your original .lrcat catalog file by double clicking on it or going to File Open Catalog inside LrC.

Suggest you submit a bug report at the Photoshop Family feedback forum. Lightroom Classic is an application from the Adobe Photoshop family. Adobe engineers follow bug reports and feature requests there.

https://feedback.photoshop.com/

I have been pondering this issue for a couple days tring to come up with something that might cause the issue you are experiences. I am unable to replicate the issue on my system.

Just thought of "Face Detection" which was added to LrC a few years ago. Do you have that feature active?

Set to 50GB with only 2.5GB worth of files in the cache folder. Library size is 136,350 images.
By @whaun2

What number of your 136,350 image files are raw file format? I would expect the Camera Raw Cache folder size to be much bigger than 2.5GB if you have mostly raw files imported into LrC. I have a mix of some JPEG, but mostly raw files. My Camera Raw Cache folder has 45,466 files with 43,355 image files imported into LrC. Check the number of files in your Camera Raw Cache folder. Try the following:

1) Go to Edit> Preferences> Performance and click on Purge Cache. You only have 2.5 GB so no big loss here!

2) Reset your LrC Preferences files as outlined at the below link, which may be corrupted and preventing the Camera Raw Cache from working properly. Place a copy of the current Preferences file on your dekstop so you can easily replace it if of no help.

https://www.lightroomqueen.com/how-do-i-reset-lightrooms-preferences/

3) Shutdown and restart your system.

It will take some time to rebuild the Camera Raw Cache so work with LrC for a few days before making any further changes.

/EDITED/AFTER EXPERIMENTATION/

In your video, I notice that you already have some basic edits in an image just imported. I also notice in your Library Module that you may have touched Quick Develop, but I have no idea if anything has actually been changed.

So, preset during import? Quick Develop?

Thing is either of those would be reflected in the History panel, in the Develop Module, at least as part of the wording in the first state, and no such wording exists.

So, how are the basic edits occurring?

Is that a clue?

Replication?

So, noticed you are using a Fuji X image, and notice you are using a DNG file. I do not know if that DNG is via LrC Import Copy as DNG, or as a result of using a third party RAW converter.

To those non Fuju X members, many Fuji X users absolutely hate Adobe Camera RAW Fuju X conversion. So we use RAW converter like Iridient X- Transformer (even if we do not sharpen at the begining, even if we do not go bonkers on sharpening)

I do not think the image being from a Fuji X nor a DNG file is the issue. But, I can attempt a replication on my MACBookPro, and a Fuji X-T3 image converted to DNG, just to be consistent

My attempt to replicate failed.

Now, one observation , and something I will need to see if I can replicate, When you go to select the camera matching profile, they are already listed (I assume you clicked on favorite for each one) , I have to browse, and select the profile, and click on close, this slows me down a bit.

Not to say having quicker access to camera matching profiles is wrong, just that it slows me down, perhaps just enough that I do not notice your issue.

Follow-up

Added Camera Pro Neg Hi V-2 as a favorite, in Library, selected a previously unedited DNG, went to Develop, selected that profile. Nope, worked quickly.