It's true that local elections often serve as a useful opportunity to "punish" the incumbent party, and in that sense the implied margins don't always translate into success at General Elections. But, firstly, there's a lot of variation about how much of a punishment a given local election is. Indeed, on more than a few occasions in the last 40-odd years, the governing party has made gains at local elections, including quite recently in 2021. Secondly, even the many local election cycles that have seen losses for the incumbents see wide variation as to the margins: in 2016 and 2018, the Tories lost only a few dozen net seats, while this would mark only the sixth time that there's been a total net loss of more than 1000 seats (I don't have percentage figures to hand, so am only dealing in absolute terms here). Those other five occasions include 1995, which appears to be the record of 2000+ seats lost and ultimately set the tone for the 1997 Election loss.
But politics is a continuing story. I think it's pretty clear that the Tories are in a seriously weak position, and have been for some time, even if they are to some extent making progress away from the dire mess they would have been in at the back end of last year. They can perhaps draw some comfort from the fact that the other heaviest local election losses I can find include 1981, 1991, and 2019, all of which come shortly before thumping General Election wins for the Tories (the final example "1000+ losses" year being 1999, for Labour).
But each of those examples exactly plays into the "continuing story" point: in 1981, Thatcher was in serious trouble, with the SDP/Libs rising fast and her economic policies in question, and then among other things the Falklands War happened; the 2019 local elections were held at a time of Brexit stalemate under Theresa May, but the December elections under Johnson instead saw the message entirely reversed leading to a famous win.
Perhaps the closest parallel to today's election is the 1991 cycle: then, as now, there had been a leadership crisis not long before the locals; then, as now, the new leader was seen as competent if perhaps uninspiring; then, as now, the new leader had to undo a disastrous, or at least a politically misjudged, economic policy shift (Truss/Kwarteng's failed budget v. Thatcher's Community Charge); then, as now, the Labour Party was still trying to clear out the leftist fringes and realign itself as a (left-of-)centre party. And, too, the margins the Tories were playing with in terms of the General Election were such that they could afford to lose quite a large handful of seats and still end up in a majority, and with a year or so between the bad locals and the coming GE.
All of this is to say that a defeat on this scale, with time still to play with, possibly isn't so bad for the Tories in the long run. It's wrong to call locals entirely meaningless -- some people do care about local issues after all, it's not unheard-of -- and they'd be foolish to carry on regardless of the results. But it could be said that the electorate enjoys firing these "warning shots", and then reacting favourably if the Government draws the right lessons from them. In 2019, that was self-evidently about ending the Brexit deadlock. In 2024, it might simply be showing that the Tories don't intend to tear themselves apart at the same time as they're supposed to be running the country.