Lightroom Classic shows too much contrast in develop module (sometimes)

After another restart the problem fixed itself. But I found an interesting article in the Adobe forums that might be related and help someone:

https://community.adobe.com/t5/lightroom-classic/lightroom-export-issues-colour-saturation/td-p/10086489?page=1

Apparently the monitor profiles can be bad and Lightroom respects the profile so it might show the image with the profile and the other applications show it without.

Use the X-Rite software to apply your calibrated profile to your display at system-level, not inside any app.
On Windows, reboot & make sure the profile was correctly applied. If you have more than one display, triple check. Windows is not good at profile handling especially with multiple monitors.
On Mac just continue, it will work as expected.

Never set Photoshop's 'Colour Settings" profile to your monitor's profile.
This is not the way it's intended to work. The monitor profile is applied between Photoshop & your screen, not inside Photoshop.

Set your working space to the one you most often need at export (then don't use it until export - though this is dependant on the next paragraph.)

If your monitor is capable of only sRGB then you will get the best workflow if you also set your camera to sRGB, rather than Adobe RGB* or even ProRes or P3 (which very very few monitors can support).
You then set Photoshop to not change profile at import - same colour settings page as for above. Set Preserve Embedded Profiles.

So, if your screen is sRGB & your photo is & remains sRGB, then you also need no conversion at export. If your display is capable of Adobe RGB & your camera saves in Adobe RGB, then at export you then export as sRGB for web or general screen use & keep your original un-converted. (Exporting for print is a different matter, ask your printer what they require.)

Every conversion gives potential for error - as you have already discovered.
Keeping your profile unchanged all the way through the entire process leaves less margin for error.

*There is great temptation to have your camera save pictures at the "best" colour setting it can; however, if your monitor cannot display this, you will never see exactly what you are editing. sRGB is a very safe default. All displays aim to cover sRGB… even if they don't quite manage it, or are badly calibrated by the factory or their owners - but that is entirely outside your control. So aim for safe.