I agree that there are enough pro-indy MSPs to vote to hold another independence referendum, and it was mentioned in the manifestos of both the Greens and the SNP so technically they have a mandate to do so. However, it would be foolish to assume that everyone who voted for these parties is in favour of independence as people vote for a variety of reasons. As with PPs, I know of several staunch unionists who voted for their SNP because they believed they had socialist credentials and were disillusioned with the Labour party. The SNP itself has sought to reassure people in the past that a vote for them was not necessarily a vote for independence, and many people believed that. After seeing that vote co-opted into support for independence I doubt they'll do so again, but we'll have to wait for the next elections to see how big an effect that has.
It's also clear that campaigning on both sides has never really stopped since 2014. The Scotland in Union movement has been more active recently, and there have been several pro-independence marches, occupations, and of course the SNP's 'listening exercise' which was less about whether people wanted another referendum and more about asking why they voted no and how the SNP could change their minds. I'm assuming the answer wasn't what they wanted to hear as there has been not a peep about it since it closed several months ago. NS herself formally put independence back on the table last June and has reiterated that position many times since, and it seems ridiculous to suggest people haven't been thrashing out the arguments even if the formal campaigns haven't yet been launched.
And no, the polls have not shifted in support of independence after Brexit. They've fluctuated a bit since 2014 and there was a tiny bounce in support for leaving the UK after the Brexit vote but this quickly settled back down. It's worth bearing in mind that the polls overestimated the yes support before the 2014 vote, with 'yes' being consistently between 47-49%, and occasionally even over 50%. On the day, people voted for what they knew as they tend to do, and it's likely that the 45-47% (with one disputed 49%) support shown currently would also be an over-estimate.
NS of course knows this, and also knows that if she lost a second time that would bury the question for a generation (a human one, not a fruit fly's). But she's painted herself into a corner with her ultimatum over her Brexit position and the statements that 'she's not bluffing'. I reckon she must be praying that TM will give any concession that she can call a victory and so postpone it. Imo, her biggest problem is that, despite stoking a fair amount of anger over Brexit and warning of 'Tory hard brexit cliff edges' etc. the Scottish people still don't support independence in large enough numbers. This is probably because while the Scots may be unhappy about the situation they are ultimately pragmatists, and they can see there are still fundamental problems such as a weak economy and no clear currency plan. It is also clear for everyone to see that if leaving the EU is bad leaving the UK must be a disaster, particularly as we would not just step into the same deal with the EU (confirmed today by a senior EU official).