My take on this is that most likely it would resolve naturally.
Sun storms only last a few hours according to an article I recently read. I don't know exactly how solar storms work but I assume that the part of Earth which is exposed to the Sun at this time will be affected most, but the opposite half will have parts which should be almost unaffected. So if we're not completely unlucky and that unaffected part is just located in Antarctica or the Central Pacific or so, then there will be at least some subnetwork ready to still run Bitcoin, even if they wouldn't be able to mine many blocks during that time.
The big problem imo would be to prevent an 51% attack if the low-difficulty phase really lasts longer than two difficulty periods, but it would also be very difficult for an attacker to realize it in such conditions. But the risk would be a little bit higher. It would be most sensible during that time to rise the number of confirmations to a very high number (100+). This would of course make Bitcoin less usable but it wouldn't be its "death".
In the case that a blackout affects the majority (60%) of the nodes and leaves only 30%-40% functional, and this happens right at the moment of the difficulty adjustment, it is highly likely that consensus issues will arise. The remaining 40% could continue producing blocks at lower difficulty, but the chain generated during that time might not be accepted by the 60% of nodes when they come back online.
If the 60% are isolated from another during the outage, then they cannot produce a longer chain than the 40% which are functional. So they will have to accept the 40% chain. The situation will not be that much different from 2021 when the Chinese miners shut down, only faster.
My thought is that on a closed reduced "fake" network, even some old Laptops could do the job ! ?? (like just connecting some machines on a single room and tricking the code to think is Internet)!
Mining doesn't work that way. The network size is irrelevant. The relevant parameter is the difficulty and the individual hashrate of each miner, which determines the number of zeroes the block hash must have. And finding a block hash with that many zeroes at the start like now, is very difficult, and only big mining farms can do it constantly and in reasonable time.
Thus, if the difficulty is high, not even if you are completely on your own you can create "fake" blocks with lower difficulty.
Filling the blocks with fake transactions would not make any difference. Empty blocks can be perfectly valid and they would also be somewhat expected in the doomsday scenario we're speculating about
