How useful are political petitions?

in Purgatory
This has been on my mind for a while--years, really. How useful are political petitions? I sign the things all the time, but I feel like anyone they're going to is already on whichever "side" of the issue they're on, and I can't see how this changes things. But are they really useful?
Comments
Of course, it is now all email.
The exhibition also features banners from the Greenham Common protests which - unlike most demonstrations - did appear to help achieve their goal of getting the nuclear cruise missiles removed.
https://museum.wales/stfagans/whatson/12152/Petitioning-for-Peace/
Beyond that very specific form of petition that very few people have an opportunity to sign, there are probably three forms of political petition in the UK that most of us are familiar with, which seem to have different effectiveness.
The first form of petition is closest to the traditional petitions of pre-internet days. Those organised by a group of people, which may be an organisation formed specifically to campaign against something, and run by that organisation. These petitions may still even be physically signed on paper, though now always supplemented by online. The effect of these petitions is almost always in the group of people turning up at their local council or even Downing Street with boxes of paper signed (and, accompanied by the media to report it), but also by coordinating efforts in other forms of campaigning - often these might be objections to a planning application, so the petitioners also encourage people to submit opinions into the planning consultation; but also writing personal letters to elected officials, marches and other forms of public protest. When a group of people put time into getting an issue raised and keeping that issue in the public eye that has power to be heard, and a petition within that context works very well - which, of course, includes a lot of sharing of the petition.
The internet has spawned several organisations that make producing petitions very easy. Many of the type of petition above are now on these platforms, but the ease of producing a petition means that many of these petitions are initiated by an individual or small group who don't follow that up with the work of promoting the petition or any of the other forms of campaigning that make petitions a part of a successful campaign. Also, these petitions being easy to start will often result in multiple versions of effectively the same petition, which dilutes the effectiveness of the petition.
Finally, the UK has a system of formal petitions to Parliament. For those that get more than 10,000 signatures this at least requires the government to respond, and over 100,000 there's a committee that then considers the petition and can put that through to debate in Parliament (which may be in committee rather than necessarily the full chamber of the Commons). This means that someone is aware of the issue, even if the responses are usually "we're not going to change anything". I'm not aware of any of the big petitions that were successful - the 6.1m who signed a petition in 2019 to revoke Article 50 were ignored, as were the 4.2m who signed a petition in 2016 (before the June 2016 public vote) calling for a threshold of 60% votes and 75% turnout for leaving the EU, a couple of petitions that between them had more than 2m signatures didn't prevent Donald Trump receiving the honours of a full state visit.
Where any petition can be most effective is when the organisations running them make a lot of political capital from the petition, and make a lot of noise about how many people signed. There's a local protest here about a development near Loch Lomond which has made a lot of noise about the campaign breaking records on number of signatures for a planning application, also "the most signatures in 48h" type of stat, along with the planning consultation. Lots of media coverage, and social media sharing of the petition and those news articles.
https://www.women.govt.nz/about-us/history-womens-suffrage-aotearoa-new-zealand