Scotland is already a separate country, technically speaking, so I don't think it's comparable with the Basque situation. Furthermore, with the UK leaving the EU, they've opened doors that non-EU members can't use to work around such issues.
I don't think it'll happen soon, but the desire for independence does seem to be there to a significant extent already: https://www.telegraph.co.uk/politics/2026/09/13/irish-scots-...
The largest problem for an independent Scotland trying to join the EU would probably be that the EU doesn't just let anyone join. You need to have a strong enough economy and a grip on national debt to join.
From independence 1922 to 1979 (when we joined the EMS) Ireland just used a currency pegged to Sterling. An independent Scotland would presumably use a newly-created currency pegged to either Sterling or the Euro, on at least a temporary basis.
Spain have dropped their threats to veto Scottish accession: https://www.theguardian.com/politics/2017/apr/02/spain-drops...
It was known that there was likely to be a Brexit referendum at the time of the Scottish referendum: Cameron had promised one if the Conservatives won the 2015 election.