As far as I know, there is no "hard and fast limit" on tiers by frame size.
However, there do seem to be "practical limits" as to how many BPs can be "spent" on the smaller frames. One way to sidestep this is to use the Squadron Combat rules to allow the PCs to use multiple ships, possibly an explorer or transport with one or two launch tubes.
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Not quite what you are asking for, but from the Example Starships list:
Tiny ships are mostly Tier 2 or under,
Small ships are generally Tier 6 or less, with a couple of outliers at Tiers 8 and 9,
Medium ships run all the way up to Tier 12,
Large ships are mostly in Tiers 4 through 13,
Huge ships are mostly Tiers 8 through 13,
Gargantuan ships are Tiers 12 through 16,
Colossal ships are Tiers 16 through 18, and
Supercolossal ships are Tiers 19 and 20.
It's been a while since I played around with customizing ships, but I seem to recall that you start to run out of available PCU (the most restrictive limitation on Tiny and Small ships, since they can't use a power core housing in an expansion bay) to power things on Tiny ships around Tier 6-8 and Small ships around Tier 10-12.
Medium ships often run out of worthwhile improvements around Tier 15-17. Example Tier 16 on an explorer frame.
If you're using Starship Operations Manual it's much easier to find useful BP to cram into a small frame. I've made tier 16 fighters (extremely hard to hurt with deflective shields and adamantine hulls, extremely undergunned because only light weapons), and you can do a worthwhile tier 20 medium ships easy. Load up on automatic quality magic missile weapons (they have a different name, they're quantum with long range and broad arc) launchers on the flanks, big linked weapons in the turret and fore/aft (put a mine layer in the aft), and you can lay out huge hurts.
Don't forget your VIs for extra actions in the tiny ships.
The tiny ships at tier 16 are just a thought experiment, they're never actually useful because of the weapon limitations. They can live a long time because of immunity to capital weapons, crazy high AC/TL from unlimited budgets for defenses, damage reduction from deflection shields and adamantine hulls. I don't have a real answer to you about when a tiny or small ship stops being practical at a given tier. I'd abandon them as soon as I can just for seating and hull point reasons. Tiny are never useable at any tier for the former reasons.
Medium ships are always viable. The full sized tier 20 magic torpedo unit has a +20 bonus that rolls twice to hit, because quantum quality. Check out the published high tier AC/TL for tier 16+ cruisers through super dreadnoughts, they aren't actually very high because of size penalities and armor costing so much past minimal levels. So with two rolls to hit the automated torpedos usually hit. Six of those (because broad arc) are firing at anything in your front or rear arc, then you only need a couple of gunners (or one gunner plus one VI, or Broadside or Fire at Will actions) to fire at no penalty your front/rear arc linked guns and turret. That's 6x17 potential damage from the magic torpedo units, 4x35 from persistent particle beams, average is 242 if everything hits. You'll put your computer bonuses in your two big guns, so they are very likely to hit, the 6 torpedos are likely to hit. If you're forced to fire into port or starboard you Broadside, which cuts three torpedos out of what you can use, but does raise your accuracy on the other three quite a bit.
Three to five rounds, any big 20 tier ship with big HP and high shields is likely dead. You're more manueverable and faster, you can usually stay out of their big gun arcs. If you can't, it will admittedly suck. That's why the CRB tells you not to fight even CR ships very often, they're deadly!
There are zero rules about officer limitations once you go past medium frame anyway, it's all random nonsense where the number of officer actions has no bearing on anything. A destroyer can have 6-20 crew, and have been published with 6-12 officer roles. No reason they could have 20 actions if some crazy Paizo employee slipped it in. Hull points (which is where medium ships really suffer, consider ablative armor in small doses at higher tier) and capital weapons (which are just BP and mount efficient versions of heavy weapons that come with significant overhead costs from frame limitations) are what matters, not crew actions, on the high tier ships.
There's also the basic option to just put three antimatter missiles in your forward arc and three in your turret on a fast, manueverable ship. Broadside gets you 6x55=330 average damage if they all hit. (This set up is why a good ship should have 1-2 point defenses in their turret, and many mid to high tier paizo ships do).
A flyby with a strong computer to maximize success (and stunt piloting is one of the easiest character optimization challenges) lets you target them in an arc that doesn't have a non-turret point defense, and a backup gunner can also dump some plasma mines (whether homing or not) in hexes fore and aft to add some extra damage if they move away (and if they don't, if homing).
I don't love this one because of the many failure points that make it struggle - you can get outmanuevered to cut your expected damage by half, a double point defense turret tanks your expected damage by up to one third, and you can even be outrun to tank it all to zero. Point blank engagements are necessary. A mix of particul beams and antimatter missiles gives you more flexibility but does lower your Big Hit potential. And if a cruiser+ with a capital weapon antimatter missile comes at you with the potential one hit kill, you'll wish your turret had a point weapon for the easy shoot down chance.
Anyway, tier 20 medium ship building is fun post-SOM. There's plenty of offense vs. defense tradeoffs to be made and tactics to exploit them. But you're still a bit of an eggshell with a (light) sledgehammer even with max shields, so probably the safest and most reliable but most boring build is to go heavy defense and armor and speed, not worry about manueverability, and just maintain max distance to ping big lumbering enemies from long distance with linked turret particle cannons boosted by a computer. You'll consistently hit, they'll have lots of weapons that suffer range penalties or are useless if you stay 15-40 hexes away. Face your aft (you can put another pair or single particle cannon there) towards them, maintain distance, and dump lots of free shields from other arcs into the aft for when they do hit. Your science officers can burn their free resolve points (and maybe an aft facing ECM, albeit with big range penalties) to hurt their accuracy.
My final forward arc favorite for close-ish range hunting is the rail quality guns that SOM introduced (but not the "railgun" in CRB). They get extra damage for extra accuracy, and at high tier with computers, attack outpacing AC/TL, and bonuses from TIMs, you can often expect to hit at +10 over AC, when these outdamage persistent particle beams. Put a linked pair in the forward arc or turret, and optimize everything around that weapon. Only downside is 10 range vs 20 on particle beam, and slightly lower damage if you don't hit AC +5.