Status Updates From Periferal (Jackpot #1)

The main protagonists of each time show little agency. Far future Wilf even less than near future Flynne. They are driven by others around them. Flynne's main contribution so far is providing a moral compass. Wilf is more believable as a worn out alcoholic than as the top class publicist he's supposed to be.

The decisive festivity in which they are supposed to identify the murderer is looming ahead.

With the help of a very detailed Wikipedia summary, The Peripheral starts making sense. A neo-noir thriller in cyberspace disguise. In essence, somebody saw something she shouldn't have and now is chased to be killed. It only took place in the future.
While time travel doesn't happen physically, the virtual cyberspace can be in the future. This anomaly started to show up in the near future, i.e. from 2023 onwards.

After a few pages, I remember why I only read Gibson's Neuromancer so far. It's so difficult to get into his worlds. I'm not sure what is going on, except for something in cyberspace. But a cyberspace with real physical consequences. From the blurb, cyberspace even spans different times now.