Plausible founder here. There's nothing automatic but you can track your campaigns with utm_campaigns manually.

Google has made sure that analytics for Google Ads works best within their own walled garden. Same with Facebook and Twitter with their Pixel products.

Instead of using the Referer header or utm parameters as intended, these large corps send obtuse random IDs (gclid, t.co/<id> links) which only they can correlate to an ad, search query or tweet using their internal database.

So until there is anti-trust action in this space towards more oppenness and competition, you're stuck with the ad provider if you want tight integration between ads and analytics.