> The right to a speedy trial may well have been incorporated against the States,
The right to a speedy trial is incorporated against the states, yes. Klopfer v. North Carolina, 386 U.S. 213 (1967).
> a speedy trial mostly seems to mean that there must be a statutory limit to how much time can pass between indictment and the start of the trial
No, it doesn’t, nor does it provide such fixed limits on its own, instead being applied lookong at reasonableness case by case. The Speedy Trial Act of 1974 providing federal limits was largely a reaction to this, rather than required by it.
I was referring to the Sixth Amendment right to a speedy trial, since the amendment itself does not set such limits, the question is: what does "a speedy trial" mean? I've not looked at case law, but ISTM that having statutory limits and remedies must be a big component of what the right actually means.
The right to a speedy trial is incorporated against the states, yes. Klopfer v. North Carolina, 386 U.S. 213 (1967).
> a speedy trial mostly seems to mean that there must be a statutory limit to how much time can pass between indictment and the start of the trial
No, it doesn’t, nor does it provide such fixed limits on its own, instead being applied lookong at reasonableness case by case. The Speedy Trial Act of 1974 providing federal limits was largely a reaction to this, rather than required by it.