I could try to find some links on that if you like, but the way I remember it is that the EU was against the idea of Scotland going it alone and EU officials actively worked to discourage any ideas that an independent Scottland would be received with open arms.
But of course, that was before Brexit and while the UK was still an EU member whose national interests were taken into consideration by other members (because EU). This is not the case now.
Still from memory -sorry for that- but when the last UK MEPs were making their parting speeches at the EU Parliament, one Scottish MEP finished his with an impassioned plea to the EU to not forget Scotland. Which I interpreted as a plea to make it easier for Scotland to join the EU if it ever gained independence from the UK.
But otherwise, Scotland was part of a former EU member, I imagine they would not necessarily use the pound (a Scottish pound would probably be weak), so they'd probably adopt the euro in a short while, there is a ton of cultural affinity with the EU, probably more than for England in some regards, etc.
Scotland for sure could get an accelerated membership process if they do decide to become independent. They could even start some of the paperwork or at least contacts before they gain the official independence, I imagine.
Before Brexit the only blocker was a unilateral declaration of independence, which will not happen. Scottish independence will most likely be a mutual separation.
And after that the Scottish budget will be hammered hard so I imagine they'd definitely want to join the EU ASAP to get help. Access to huge markets for exports, cheaper imports, EU funding for developing regions, etc.
And we have "God's Own Country"[4] which is a phrase but does have an independence movement[5], and a region (Mercia) which hasn't been a place since 527-897CE but still has an independence movement[6].
[1] https://en.wikipedia.org/wiki/Black_Country
[3] https://en.wikipedia.org/wiki/West_Country
[4] https://en.wikipedia.org/wiki/God's_Own_Country#Yorkshire
[5] https://i-yorkshire.com/yorkshire-independence/
[6] https://independentmercia.org/declaration-of-independence/
But all that was at its apex years ago now it’s more stable.