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Covert ops breakthroughs may be worth it. Some breakthroughs might be worth it, e.g. the instant excavation can allow excavating a power coil on the third level which is a big boost to developing the Avenger. +1 to a weapon type is also tempting.
AFAIK, breakthroughs always take 10 days on Legendary regardless of how many scientists you have. If you get offered a good breakthrough right at the beginning before you have gained any scientists it may be worth it since the amount of research foregone is less than if you had a breakthrough later.
Some of them are next to worthless, they amount to trading 10 days of research for 75 supplies. Or even less in some cases.
But the plus damage ones in my opinion are worth it, unless you are in a situation where you absolutely need to make progress on something else and can't afford any delays. In general, they are all nice to have, none of them are necessary. I generally take all damage breakthroughs as a way to add some short-term challenge with a long-term payoff. Short-term pain for being behind in the really important research, long-term glory.
It can also be nice, if you have a good Breakthrough Covert Op (where you need to send a scientist) to also get a Breakthrough in the regular research lab. Because the time is fixed regardless of how many scientists you have, so you aren't losing anything by having 1 away on a covert op. And you can effectively get 2 nice-to-have buffs done at the cost of only the standard delay of 1.
So many are extremely worth it. There's some that aren't like halfling building cost and whatnot though.
There is continent bonus(random)which decreases research time if you have lab it also slightly reduce breakthrough research time to 9days at least it did in 2021 game version on Legend.
Instant exacavation can be worth it especially for the last level saving tons of time.
Reduced buildings cost is alway crap and most things are not worth the time especially on Legend.
Having a lab built makes inspirations and breakthoughs happen more often.