IMHO this works differently in countries with first past the post (UK, US) vs those with more proportional systems (most of the rest of the world). But even the latter still elect fascists.
For example, in the UK, Labour are almost certain to win in the UK in 2024. While the Conservatives will likely field a Trump-alike in 2029.
That didn't work for them in 2001 (they did nearly as badly as in Labour's 1997 landslide), but New Labour were lucky on the economy. As it turns out that was a mirage.
It took a long time for them to find somebody electable; David Cameron started off as a genuine centrist, but as soon as the financial crisis hit, he became a slash-and-burn austeritarian. Which at the time sold well, but caused many of today's problems, including in purely economic terms (e.g. economic disengagement resulting directly from NHS waiting lists).
If Starmer is unlucky, or incompetent, or deliberately supports austerity for reasons best known to himself, there's a real possibility the UK could join the numerous European countries to have elected far right governments in 2029.
The "ratchet mechanism", where the right go further right and the left calibrate their "centrism" slightly to the left of the current right, and slightly more competent, inevitably leads to more fascism and more climate catastrophe. In most constituencies, at most voting slows this down a little, but it doesn't stop it.
While it is possible to bootstrap a third party, it will take at least another decade for the Greens to be significant, while the Liberal Democrats messed up their last attempt to get proportional representation, and may finally recover this election from the extended punishment for their breaking promises in coalition.
So of course I'll vote Labour, tactically, to get the tory out. Were I in another constituency I might vote differently.
But my bottom line is that the only way to really change anything is a broad campaign including non-violent direct action. There is ample evidence that it can change public *priorities*. According to polling, mostly the public agree on the actual facts on e.g. climate change policy. But they're easily distracted.
The art of politics is seemingly in distracting people from the real causes of problems (almost always either climate change or right wing governments) while inventing fake solutions to imaginary problems (e.g. the so-called refugee crisis, ridiculous claims that the way to cut cost of living is yet more fossil fuels, etc) in order to take more power. That is true for mainstream politics but it's even more true for the authoritarian fascist playbook politics that we see lately.
Neither party will deliver the radical action necessary to solve our various major crises, most of which are closely connected to the climate and biodiversity crisis (the most obvious example is the cost of living crisis, fueled by fossil fuel prices, fossil fuel funded wars, and climate affected food prices).
Only one party is an imminent threat to democracy, but it's bound to get back in sooner or later in a first-past-the-post system where the choices available are dictated by arbitrary economic dogma that the public don't even believe in. But still, PR won't solve our problems either, it'll just make it easier to use the electoral system for real change ... eventually.
So no, I don't personally see more engagement with the *party machinery* as the key next step. More engagement with politics more generally, yes.