Spoilers Ahead!
> betting their existence on a species they knew already uses MAD
If ant colonies depend on MAD for continued existence, it means nothing to us. This example was used multiple times throughout the series. They didn't even make a singular bet on Earth. The invasion was just one avenue they chose for survival.
> You don't have to invade a system, you can send a stealthy probe.
In the dark forest of the three body universe you could send a probe, but you learn nothing if it finds no life in a system. The only reliable, actionable information a probe can provide you is if life is found. Finding an absence of life just as easily means that the life in the system is so far advanced beyond you that you cannot detect it. It would be far riskier to bet your future on a system in which you found no life. Not to mention that you are making a huge gamble on the stealthiness of said probe. The probe could be the very thing that makes you the target of a dark forest strike. Earth already appeared safe, so why take further action that carries real risk of notifying some other civilization that you exist? You can't be reliably stealthy because some other race can be technically beyond you.
> Send a big meteor
Earth was an un-imaginable eden to Tri-Solaris, it's made clear that they wanted the planet intact.
> or make a deadly disease that looks like flu
This requires a much longer timeline as multiple trips are required to carry out the plan. The Tri-Solarans were facing a very real threat of extinction that made a shorter plan worth the risk. It's made very clear that they did not wish to exterminate humanity.
Earth was valuable because in all probability the rest of the universe did not know it existed. Given that you are saying they were stupid for not building space habitats, you must not be aware of what actually happened to the Tri-Solarans :). Besides, those space habitats present their own form of danger to their inhabitants. Actually, the danger they pose is worse than existing on a planet.