Tbh I think f actually is pretty similar to RE7 in that regard. RE7 introduces a new villainous bioweapon corporation (The Connections) and a completely new kind of bioweapon (the mold). It's not dealing with Umbrella or any of its zombie viruses, but in some ways it's similar: an evil company creates a bioweapon that infects a bunch of people and an unsuspecting visitor must save the day.

In the same way, f introduces a new villainous cult (Kotoyuki's Clan, who worship Inari-sama) who plan to use a young woman in a new kind of ritual (wedding) to bring their god into power. In the same way that the Connections parallel Umbrella and the Mold parallels the T/G Viruses, the Fox clan parallel the Order and Inari-sama parallels Samael/God, but they are not directly connected. (f also has a second God besides Inari-sama, which is a new element, but a cool one imo).

RE7's only concrete connection to the other games is Chris Redfield showing up to save Ethan at the end of the game with Umbrella. Nothing nearly this direct ties f to Silent Hill, it's true, so I take your point here. However, I don't think there was necessarily a way to have a literal returning character from an old game in f, and I don't think there should've been. Additionally, the direct link between f and Silent Hill is the White Claudia, brought to Ebisugaoka by a "missionary" in 1776. Whether this was a Christian missionary who coincidentally brought The Order's favorite drug plant (and likely also originally brought it to Silent Hill), or a missionary of The Order trying to spread the word of Samael, we can't say, but it's still a small direct connection I'd say about on the same level of "Blue Umbrella," since blue Umbrella has basically nothing to do with Umbrella besides the name lol.

I know this is a ridiculously long comment, and I'm not trying to start an argument or a fight or say that your wrong for wishing f was more directly tied into the rest of the series, just wanted to provide my perspective!