Thanks for trying to help me, this instance is private but accessible directly from the internet (if needed I can give you the link). I didn't do any CSS customization I only touched the setting file (to disable some search engine and define a default language).
Where I'm surprised, I deleted my Docker searxng container (running on a Debian VPS), I deleted the images etc.. I recreated my container from 0 (I only kept the setting file) and the problem remains the same...

The problem appeared spontaneously overnight (I have a daily container purge with a latest pull).

Have you tried to clear the browser cache?
The CSS has changed few days ago : #2740

I feel like an idiot, for me I had cleared this hypothesis by blocking the browser cache with the Firefox inspection tool (and the problem was present), I've just opened a private browsing window without conviction and indeed it was the cache that was the source of my problem! I'm sorry for the lost time, thanks again for the help, you're great. I hope my case will be useful to others!
I haven't tested it on my PC browser (only on my phone) but there's no reason for it to be anything else.

You can set this value to true in settings.yml :

However you have to configure Apache / nginx / whatever to deal with the ?<hash of the content>. It may work with URL rewrite, I'm not sure, or you can configure uwsgi to serve the static file as it is done in the Docker image :

See

• static files: add a hash as a query #932 (comment)
• [interim fix] static files can't be delivered by HTTP. #995

As described, it becomes easily complicated to deal with the query parameter and the reverse proxy, but one of the above suggestions might work for you.

I had exactly the same problem. Running Searxng on Docker and accesing it through Cloudflare tunnel. I tried to use private browsing window, but didn't help. I tried to access the instance by the server LAN ip address and then the problem went away. So for some reason the problem only occurs when accessing the instance through Cloudflare tunnel.
Changing the static_use_hash to true solved the problem for me.