I think the first thing to grasp is that Brexit fundamentally altered the case for Scottish independence. You have to remember that Scotland voted for the UK to remain in the EU, not for Scotland to remain alone if the rest of the UK left.
When both Scotland and the rest of the UK were in the EU, there would have been no customs border between the two, even after independence. After Brexit, for Scotland to rejoin the EU would have meant a customs border applicable to two thirds of Scottish trade.
It would also have precluded continuance of the UK Free Travel Area, since there is free movement of people inside the EU and the FTA would have negated any UK policy to control immigration. Obviously, the UK would not allow this. (Ireland was able to remain in the CTA because as an old EU member it was not obliged to join Schengen; new members are obliged to join). In other words, Scots could no longer expect to move south freely in pursuit of economic opportunities.
New members of the EU (including Scotland) are also expected to have managed their own currency competently for two years and to commit to joining the Euro. As an old member, the UK had an exemption. Scotland has no currency of its own, nor any separate central bank. Using sterling as a foreign currency would be possible, but would not qualify Scotland for EU admission.
New members of the EU are expected to achieve a fiscal deficit target that Scotland would need about ten years of austerity to achieve, according to the Wilson Report. This would be particularly acute if the UK immediately cut off Barnett funding, stopped military expenditure in Scotland, and declined to continue the currency union, all of which would have been perfectly legitimate.
Thus, it was improbable that an independent Scotland could make a swift return to the EU, and independence would mean standing alone for at least a decade.
In spite of this, the SNP continued to agitate for independence and to neglect the day job of actually running an efficient devolved administration. The results eventually became too obvious to ignore.
Additionally, after the coalition with the Greens, the SNP began to pursue a whole agenda of politically correct policies which did not resonate with the Scottish electorate at large.
To this you have to add the impact of various scandals. The burdens accumulated until they could no longer be borne.
But I think you are wrong to see the Labour Party as pro-Brexit. Starmer was one who campaigned for a second referendum, and is still not trusted to not make unnecessary concessions to the EU in trade negotiations.
In short, Brexit did not figure highly in the list of reasons for voters abandoning the SNP.
