The Angels being buyers gives the SF Giants even more competition on the pitching market
In addition to prices being set a bit higher than they would like, the Giants now have even more competition on the trade market in the demographics that they are interested in. Before the Angels made their intentions known to be buyers, most of the playoff contenders were looking for starting pitcher depth because, well, every contender is looking for that every year.
While the pitching market is certainly more robust than the bats at the trade deadline this year, the supply is certainly not enough to meet the demand as several of the really bad teams that should be sellers just don't have a ton of talent to deal (looking at you, Rockies, Athletics, and Royals). There are some options available, but contenders need real upgrades. Warm bodies are not going to get it done and Angels just made the supply even smaller with the two arms they snatched up.
Aside from the supply side problems, the Angels have also made the demand higher when they officially entered the fray. Sure, they made the move already, but they are also probably not done yet. The Angels are already rumored to be talking to the Nationals about a trade for Jeimer Candelario and probably need to add more pitching help as well.
Unfortunately, that means yet another team that the Giants are going to have to bid against. Adding one more team to the mix isn't usually the biggest of deals, but adding one more very aggressive team to an already crowded buyers market could make targeting specific players problematic.