If the goal is to make an organized team with limited slots more willing to pick a sentinel or two over a blaster or scrapper or a defender, that won't happen easily without contorting it into something unrecognizable, and also stepping on the toes of the ATs that are more overtly designed for team play and have sacrificed effectiveness elsewhere as a result. More to the point, is that even an objective that is worth pursuing? Would that make the AT more fun, more desirable for those who choose it? What are you willing to give up, remove from Sentinel's existing kit and identity, for the perceived better shot at being picked for the kickball team?
ATs that work best in teams to blow through fights roided up on buffs is a crowded space. Sentinels don't fit neatly into that picture...and that's okay. That's why some people gravitate towards it. It's why I do. I think about my Blasters that I dump a billion inf into, expend countless valuable slots and power picks and incarnates, just so it can pretend to approach the resilience my Sentinels get just by existing, and it still gets shredded by cascading debuffs my Sentinels would have shrugged off, and I think I like my Sentinels better.
That resilience isn't as valuable in an "optimal" team setting where damage dealers should be fairly safe, but it's highly valuable virtually everywhere else.
That said, Sentinels do suffer from negative perceptions that could mostly be attributed to what it was like when it first launched. As a relatively new player who glommed onto Sentinel as my "main" AT starting out, I missed most of that negativity but it's easy to still see the fallout from it even to this day. At this point, however, I feel like it's more of a perception issue than anything else.
The more I think about it, the more I feel what Vuln fundamentally does right now, that is pick out a single target to soften it up, is good. Niche? Yes, but niche is good, niche is specialized, and balanced and affords more room for buffs. Rewarding some manner of stacking buff for the Sentinel and teammates prioritizing the target wouldn't be unwelcome as an addition to what vuln already does, and this separate addition could be scaled to allow for stacking by multiple Sentinels, where the numbers would be capped but multiple Sentinel vuln make the ramp-up quicker. Making the buff something like recharge speed would be valuable and thematic, though possibly overpowered. Something like, Vuln does what it does now, but hitting the target with an ST gives the attacker a stacking +x% recharge time buff, capped at anywhere from 10-30%. Multiple Sentinel vuln applied to the same target gives more increments of the stacking effect but doesn't move the cap. I can't speak to how feasible something like this would be to implement, but it does in my mind represent an attractive boost to what a Sentinel could do without messing with what it already can do.