I believe the statements that appear here and on Patriots.win do not get the same widespread coverage as, for example, President Trump's appearances on Fox or his tweets did.

Because these statements are targeted at his voter base (mailing list and all), while appearances on Fox and tweets are public (in the sense that there's no barrier to seeing them). Appearances in TV and tweets will always get more coverage than an email to his voters.

these image statements are seemingly meant to reassure Trump's hardcore audience that he hasn't lost sight of the main goal: bringing to justice those who interfered in our 2020 election.

You are following the correct line of thought - these are targeted at his hardcore audience to reassure them - but you're not reaching the conclusion: that he's doing this to secure votes for 2024. It's made to appear like he's doing something about 2020, when in fact it's to keep the carrot on a stick all the way up to 2024. It may look like I'm assuming 'malicious intent' on his part on this, but I'm not: rather this is what politicians do, and he's one.

these image statements to the effect of, "by the way, I made the vaccine possible, it was all me," and it's concerning because it's directed at us, not the general public at large.

And the conclusion is...? That his anti-vaccine voters aren't as relevant (or crucial) to him as the vaccinated ones - in the sense that he's risking losing these in favor of those. Or rather, aren't as important to his public image before society at large and media. Politicians are all about public image and building narratives to their voters, afterall. And he is a politician - not just any politician, as he was president, so a big politician actually. Does this sound plausible to you? (honest question, not rhetoric).