Intelligence is probably the best butterfly that came out of this timeline. So much good has come out of that show and it's only going to bleed into TNG and subsequent shows. I think a lot of Trekkies will rightfully cite it as one of the most influential shows in the franchise, roughly on the same caliber as TOS or TNG in terms of characters and plot.
It’ll have a ton of impact on TNG and DS9
—The Romulan isolation mentioned in Season 1 of TNG is butterflied. At the very minimum, Starfleet Intelligence agents are always interacting with the Tal Shiar
—Karlax will be a recurring character on both TNG and DS9. Uhura will make a cameo in TNG
—Karlax‘s experiences will be important to Worf
—The Klingon intelligence apparatus will receive a greater role in TNG and DS9. For example, the House of Duras could control the loyalty of many Klingon intelligence agents in TNG
—Some of the 24th century Trek aliens (Betazoids, Ferengi, Breen) were introduced in SI so it acts as a bridge to the future Treks
—Likely no Section 31 ITTL, Intelligence is good enough to do whatever it needs. There could be a rogue Starfleet Intelligence apparatus or rogue agents but it won’t be called Section 31
—Starfleet Intelligence will reveal the existence of the Dominion
—The nanoprobe virus briefly mentioned as an attempt to kill the Borg in BOBW could be part of an episode plot in TNG, and the morals behind it would really make it a quandary for Picard, who was assimilated and would love revenge, but it violates Federation ideals
Among other things
In terms of its impact on the 1980s television scene, Starfleet Intelligence is about as critically acclaimed as Hill Street Blues