Pirelli has insane exposure in motosports. They also got a lot of exposure from Inter especially during the late 90s to early 2000s when Moratti was spending like crazy and we had top players like Ronaldo, Vieri, Zanetti, Pagliuca, Simeone, Seedorf and so on. After a while it became automatic, people assumed that there was some symbiotic relationship there.
But Pirelli does not need Inter to sell their shit. From F1 alone they receive more than enough exposure. They also sponsor the Ice Hockey world championship which probably covers a population that doesn't care much about F1 (central and northern Europe, USA, Canada and Russia) Inter was more like a childhood derived gesture from Provera.
And for the most part, their sponsorship deal was one of the highest in the world. That changed when FFP was implemented and teams started to use some sort of money laundering practices (or government sportwashing) to fill up their revenue streams.
Until the late 2000s, Pirelli was probably amongst the top 5-10 of sponsor deals for the most part of the decade.
Then in the 2010s you had Fly Emirates (UAE), Qatar Airways (Qatar), Etihad Airways (UAE), T-Mobile (Germany), Gazprom (Russia) from government deals and the PL was flooded with betting company sponsors. Juventus started using their owners' company on the shirt, which was a practice used by others as well, since they couldn't pump money otherwise. Teams like PSV, Leverkusen, Wolfsburg, Hoffenheim, Sassuolo, Leicester etc did this.
Some teams like us, kept regional businesses sponsoring for the most part, like Inter, Dortmund (Evonik), Parma (Parmalat) etc
The main "normal" companies that were sponsoring sports in the 2000s were the likes of Siemens, who are pumped by the German government as well, Samsung with some other Asian electronics companies, telecommunications companies and big beer companies like Carlsberg, Heineken etc, car companies or some banks until the mid/late 2000s.
It was a much more normalized period for shirt sponsorships. And Pirelli was amongst the gods. The reason was that Pirelli was also quite unique to us, I don't recall another side having Pirelli as sponsors, but Milan for example had Open and then B-Win before switching to Fly Emirates which was shared with Chelsea, Arsenal, PSG, Real Madrid and a few others in that chronological order. They also shared B-Win with Real Madrid iirc.
So Pirelli made Inter's jersey unique as well, we shouldn't underestimate that. So you felt that there was some special relation there. I'm not going to say it filled anyone with pride, but when you consider that a company just throws money at some team and yet here you are with a family business that sticks with you for a couple of decades, it just rings differently.
Nowadays there's not as much interest in keeping up with the prices so you still see betting companies, crypto scam platforms and the typical government sportwashers. Betting companies sponsoring teams are illegal in Italy iirc, I've no idea why crypto platforms still aren't since CFD providers are capped for a minimal amount and cannot be anything more than a relatively silent partner, so I trust that they'll soon ban Binance, Crypto.com, Digital Bits, Socios and whatever other shit Serie A teams and the league have as main sponsors now. And Italy is not really in luck with getting these government sportwashing deals. The big Italian businesses aren't interest in football either because it's corrupt or because their customers have nothing to do with the sport. I cannot see companies like Ferrero or Prada sponsoring a top side anytime soon, unless one of their heirs is a fan of a team and wants to buy it and just uses this as a means to pump funds into the club.