I think it depends on the country. If you click on their instructions for different countries—Itally, for example—they have screenshots that show needing a document number like a Personal ID card.

No, not for the vast majority of EU States, no, it requires an actual official government id like the EU eID, your tax ID number, something like that.

From Belgium it was also necessary to provide your social security number. And as more EU countries are moving towards e-id, I would assume there will be a negligible amount of non-EU signings.

Poland requires DigitalID or PESEL (National Identification Number, kinda like SSN for the yanks) number.

For me i had to write my personal number which is not something you could just guess on the fly so i dont think its so easy to fake signatures.

I was asked for my ID number for Portugal.

then buy 60 senators for a bag of bubblegum and two spools of string.

The old senators will think that’s a good deal.

They had the "We the people" platform, started by Obama. But Trump started ripping it apart, and Biden pulled the plug on his first day in the office.

And even then instead of being people driven, the US administration would choose what they want to address or not. For all the excesses of EU bureaucracy, there are plenty cases like this where it prevents politicians from ignoring people's concerns; they can still refuse to act, but at least the petition system forces them to go on record.

Many US states have official citizens initiatives systems, but not on the Federal level, no.

Some states allow citizens to propose ballot measures if they get enough support, which then get put up to vote in the next election and become law, but both parties hate the practice and fight it wherever they can. No such thing exists at a national level though.