I fully disagree here. QIth CT/MT:HG, most mission killed ships are easily recoverable and, with TCS rules, repairable. It's Narrative, not Rules, that say they were too badly trashed (or outright destroyed)
OK, let's do a detailed look instead. I think you might be right:
You have engaged the enemy. Presumably you are victorious, driving the enemy from the field as it were, since you're considering salvaging his wrecks.
As pointed out, the T-Meson inflicts 19 internal and 19 radiation hits. We've got fiber optic backups so, other than a possible critical, mostly the radiation killed crew; there were likely a couple of Weapon-3 or 4 hits. Fuel tanks were shattered - likely twice but that makes no difference; they can be repaired easily, if I read the TCS rules correctly.
We will accept that 12% of the opposing battlecraft hit by spinal meson fire are fragments; some of yours are as well. For each of the remaining craft hit by spinal meson fire, on average three other systems are destroyed by internal hits and will have to be replaced (unless we were lucky and it hit the crew or troops or frozen watch instead): among those crits, ~42% chance the jump drive was destroyed (if it had one), ~30% chance the power plant was destroyed, overall 60% will need a salvage tender. ~23% chance the computer was destroyed, ~16% chance the bridge was destroyed, so about 14% will need a piggyback. Overall, about a quarter can travel under their own power to a place for repair, assuming they're jump-capable in the first place, and the rest will either need help or will need to be repaired there.
Now, here's where things get interesting: unless you vastly overwhelmed him or were very lucky, you've got craft in the same condition. Unless the opponent was at the same tech level, your top priority is to repair your own craft; higher tech ships may be a problem for you if you don't have the tech to repair them, no point in repairing lower tech ships until you get your own better ships back in the fight. Where they can't be made to jump by piggyback, your salvage tenders are coming out, collecting them, and delivering them to your Class A/B starport for repairs. The tech level rule will cause some headaches here; you may need to travel a ways if you've got high tech ships, since high tech A/B worlds are rarer than the other sorts. The whole of the Marches has four TL15 worlds, all some distance from the border with the Zhodani; your situation may be better depending on the size of your map. On the other hand, the lower tech enemy ships can be taken to your lower tech ports if you can get them there; the Marches has three TL14 worlds.
Damaged battleriders are easiest; yours can travel back on their own tenders. You'll have to reorganize a bit so surviving riders can move forward to the next fight with as few tenders as possible to leave the others for salvage work; or, you give up the initiative and leave them there so your tenders can grab salvage, which might be risky. You likely don't have any enemy tenders but riders are smaller so salvaging enemy riders is easier. For larger craft, a lot depends on how much you invested in building salvage tenders: you anticipate needing the things, but the more you spend on them, the less you spend on combat ships.
Shipyards have a damage capacity more or less equal to their population, modified by a government type modifier. The average planet has a population of about 342 million just from the pop code, but that's heavily weighted: only about 1 in 6 worlds has a population in the hundreds of millions or better. Still, that's a generous capacity - a pop 5 world with a good starport and the right tech level might be able to repair a battleship and certainly could repair cruisers and battle riders - and craft are likely to be fully repaired in a couple of months. The real constraint is that tech level rule: the higher your tech level, the farther you're needing to transport craft for repair and the longer it will take to get there (and back). Alternately, once the message arrives (high jump couriers accompanying your fleet will be useful), the port's sending out parts that can be transported to stricken craft (high jump transports might be useful) and installed. (Presumably the naval base is sending replacement crew unless you came prepared). It takes "double the normal repair time". I presume the crew is working on all systems more or less simultaneously, but it doesn't actually say, so 2 to 4 months. Things like the maneuver drive could likely be brought in from ports a lot closer since they require a lower tech level.
So, much depends on the flow of battle. If you're winning, you'll likely have time to repair most of the enemy's stricken craft and add them to your fleet, but it may be several months depending on how far away the source of parts is. There doesn't seem to be a rule on how many parts can get made (or I missed it). If the war is more or less balanced and that world's hotly contested, you'll be working your best to get out your own crippled ships for repair first, and the rest are likely to face an Invasion Earth scenario, with hastily repaired cripples adding their strength to whatever forces you've got in that system. If you're smart, you brought a bunch of spare crews in cold sleep in transports; those transports could always have jumped away from the original battle if it had turned against you, but they'd be invaluable if you won, providing crews for all those crippled ships so the field repairs can get started right away. Some cripples will be of no use - dead powerplants and such - but pretty much anything with power and surviving weapons might be able to help a little, at least for a while - presumably including enemy cripples if you brought enough crew. The patched up enemy cripples could actually be quite valuable in your effort to hold the conquered system, assuming you invested a bit in sleeper ships for that occasion.
Might get a little complicated, what with the little couriers and transports and calculating cargo space and all, unless you and your opponent agree to abstract that and just say it takes X time based on the distance.