Generally BA will only upgrade if a cabin is overbooked but there is a thing called DUT. (Discretionary Upgrade Tool) The higher up you are status wise then generally better your chances but from what I've read here over the years it's not as always straightforward as one might think. Ive had a few upgrades as a Gold from WTP to CW (LAX) but as i was a solo traveller, HBO. I believe its easier for BA to upgrade solo travellers.

However I believe the system can sometimes also work in favour of other statuses to tempt someone into booking CW in future after getting a 'taste' for the upgraded cabin.

Here's a few articles worth reading which might explain it better. I generally think though it's best to forget about it and if you get a beep at the gate or even beforehand on the App then it's a very pleasant surprise.

https://thepointsguy.co.uk/news/how-to-get-an-upgrade/

Here's a very worthwhile post by the highly experienced man himself, corporate-wage-slave.

An older post but i believe it's still the same.

https://www.flyertalk.com/forum/27985949-post2.html