If we're discussing democratic mandates, then it's worth recalling that Castillo polled 19% of the vote in the first round and won the runoff with a margin of 0.3pts. Enough to be the constitutionally and electorally legitimate President, certainly, but not enough to claim much of a mandate for radical political action let alone radical constitutional tinkering let alone an attempt to pull off an Autogolpe. I would suggest that the whole experience - and, frankly, the whole experience of Peruvian politics over the past few decades,* suggests that an Executive Presidency is not a good idea for the country.
*Every single elected President has ended up in prison or ought to have done: Garcia avoided it by topping himself like an Agatha Christie villain and Toledo has been trying to dodge it - but presumably will fail in the end as he lost that case last year - by hiding out in the United States.
I think that some of the issue is their top-two system. Castillo got about 19% and Keiko Fujimori got about 13.5%, then Peruvians got to pick and, as they did in the previous two elections, Keiko lost by under 1%. I wonder how it would’ve gone if there was an instant runoff system instead.
In a way, Peru’s politics are starting to remind me of Israel’s in the sense that there’s constant turnover, splintering coalitions/parties, and bare majorities either for or against a polarizing figure (Keiko Fujimori vs Bibi Netanyahu).
Under AV ('instant runoff') the winner would likely have been either Rafael López Aliaga or Hernando de Soto. It almost certainly wouldn't have been either Castillo or (especially) Fujimori, probably the two most unpopular candidates.
The difference is that while Israeli politics is multi-polarized around clear sectarian poles, the South American runoff presidential system incentivizes every "flavor of the year" Caudillo politician with a following to try for the top office, leading to voter depolarization.
It's more a distinctly Peruvian than South American problem. Over a period of many years, pretty much every political movement (most notably APRA) in the country was discredited, culminating in the falls of both Kuczynski and the Fujimoris in 2018. This left Peru with no political parties or political actors capable of uniting even 15-20% of electors behind them, and therefore no incentive for politicians to band together to win over a decent chunk of the electorate.
Ironically, it looks as though Keiko Fujimori was basically propping up the system for a number of years, as Fujimorismo had a strong following and a high floor, forcing other ideological strands to unite behind a single politician, rather than splintering off all over the place.
Other South American countries certainly have the potential to go down this route, but it's only Peru which has done so far.
The most sensible thing, not just for Peru, but for virtually every country in Latin America, is almost certainly to abandon Presidentialism, but that is very unlikely to happen.