She is allowed to veto proposed legislation, and potentially actually exerts some influence thereby - exactly how much remains a secret https://www.theguardian.com/uk/2013/jan/14/secret-papers-roy...

At this point I'm not sure if UK can do much to avoid a major constitutional crisis one way or another. The deal would be seen as betrayal of Brexit by most its supporters, and remaining even more so. Hard exit would make a mess in Northern Ireland, for starters, and then you have Scotland, and not to forget that Remainers actually make the majority of the population in UK as a whole at this point.

Historically, things haven’t ended well for monarchs who tried to act independently of parliament.

https://en.m.wikipedia.org/wiki/Charles_I_of_England

The fun one is the right to shut down the entire house of commons, including the prime minister. That leaves her running the whole show pretty much, though oddly without the right to raise funds via taxes.

Was this legislation to avoid situations like the tyrannical Prince John of Robin Hood fame who just taxed and taxed to line his own pockets?

I'm not sure, but I think it had to do with paying for fighting the French.