This one is a known Shopify admin quirk, not something you are doing wrong. The product saved fine, the bar is just lying about it.
The usual cause is category metafields. When a product has a product category set, Shopify auto-adds the metafield definitions for that category, and any that are empty can make the form read as “changed” the moment the page loads, before you touch anything. So it shows Unsaved changes and makes you hit Save on a product you never edited.
A few things to try, cheapest first:
Open one of the products it happens on and scroll to the category and metafields section. If you see auto-suggested category metafields sitting empty, that is the likely trigger. You can turn the auto-suggested ones off under Settings, then Custom data, then Products, so they stop getting attached on open.
Do a hard reload on that product page (Cmd/Ctrl plus Shift plus R). A stale cached admin bundle causes the same phantom-changes behavior, and a hard reload clears it. If it goes away after that, it was the cache.
Test it in an incognito window with your browser extensions off. Some extensions modify the admin DOM and trip the unsaved-changes detector. If incognito is clean, an extension is the cause.
One thing worth knowing: in every version of this I have seen, the product is actually saving. The bar is a false positive, so you are not losing data by navigating away. Annoying, but not dangerous.
If none of that sticks, it is worth a bug report to Shopify support with a screen recording, because this has been reported on and off for a while and they do track the repeat cases.