How can the constitutionality of impeaching a former president be determined?

I’d agree that a simple legislative action to deprive a former president of pension and protection would be legally questionable at best, but upon impeachment and conviction, I would think they could be revoked as being part of an “office of honor, trust or profit.” As @Little_Nemo points out, it’s not really a “pension” as normally understood, but more of an ongoing salary - it sure seems like it’s of profit. I suppose one could argue it’s not actually an “office”, and so outside the scope of the judgements available.

Does anyone know: have any federal officers who have been impeached and removed had a pension revoked as part of the judgement (without a criminal conviction)?

It’s not in their original jurisdiction, so no. if the issue is justiciable, it would have to be raised in the lower federal courts first and work its way up.

For instance, let’s assume the Senate convicts, and then disqualifies Trump from ever holding federal office again.

In 2024, Trump puts his name down in the primaries in all 50 states for the GOP nomination.

But one of the states (let’s say Georgia, just for S&G) has passed an amendment to their election statute which states that “No person who has been disqualified by the Senate from holding federal office is eligible to be nominated in the state primary for a presidential nomination.”

And then the Secretary of State for Georgia, let’s pick a hypothetical name, like say, Raffensberger, writes a letter to Mr Trump, advising that he is regretfully declining to put Mr Trump on the ballot, in light of his disqualification by the Senate, and ends the letter with a polite “Nyaah, nyaah!”

So Mr Trump then starts an action in Federal District Court, seeking to have mandamus issue to have his name put on the ballot, because Raffensberger has infringed Trump’s rights under the federal Constitution.

Now, whether the District Court will rule on the issue or not is a question, given the political questions doctrine, but it would start in District Court, and then have to work its way up to the Supremes.