I don't know how these events are conducted, but I'm assuming that it is
not simply each player playing from home unsupervised. That would make it way too hard to prevent cheating. So I assume that there is a tournament official onsite at each player location watching, just like there would be for an in-person tournament.
If that is the case, there are a couple of reasonable ways to handle this.
One is to bring back something that used to be common in high level chess: the adjournment.
This used to be common when most championships used time controls that were slow enough that you often would not finish the game in one play session.
The way it worked is that at the end of the play session, the arbiter calls for an adjournment. When the player on the move decides their next move they write it down on a piece of paper rather than actually making it on the board, the move is sealed in an envelope which is kept by the arbiter, and play stops.
When it is time to resume, the arbiter opens the envelope and plays the sealed moved on the board and starts the clocks.
Both players are free to analyze as much as they want between play sessions, and can get outside help. For world championships, especially back when it was Fischer vs. Spassky or Korchnoi vs. Karpov and the match was serving as a proxy for the cold war, each player would have whole teams of top GMs to help analyze during an adjournment.
The player who sealed the move has the advantage of knowing for certain what position will be on the board when the game resumes. On the other hand, the other player is going to be the first one to have the move after several GMs have pulled an all-nighter analyzing it for them so any inaccuracy in the sealed move is much more likely to be punished than it would have been without adjournment.
Or get a freaking modem. Exchanging chess moves does not require high bandwidth, and most of these internet outages do not take out phone service.
Do a mini-adjournment (seal the move, but keep the players on site), establish a dial-up connection between the playing sites, and then unseal the move and resume.