Cross-device browser sync behaves weirdly as of late

I've seen 2 things that I found odd in the last 2 days. A note that I use Chrome for work and Safari for personal things, and I have 2 user accounts on my Mac, one for work and one for personal.

In the last few days I'm noticing that tabs opened on Safari on one device don't really sync to the other one (both from mac to phone but the other way, too). By "don't sync" I mean I open the new tab window and the tabs aren't available in the "other devices" section. For example right now I'm typing this post on Mac, Safari. I open my phone and this tab isn't visible in Safari. So sync is just not reliable.

To my surprise, today I had a Safari tab open on my phone and instantaneously it appeared in the dock on my Mac in the work account. Weirdly though, it appeared with a Chrome link, not a Safari link. I open Safari and I don't see the page even suggested. I don't think this used to happen. Chrome is the default browser for the user, if that makes a difference.

So Q is, do you see any of the 2 points above as expected behaviour? I feel something's changed and I wonder if I'm not following developments or it's a bug.

Thank you very much for reading!