Not much I don't believe and this is coming from person who still enjoys and follows Overwatch and its esport. Overwatch League (tier 1 esport) NA/West games average at around 50k on YouTube (exclusive) per game currently, I don't know about APAC but at least lower YouTube numbers. First day of OWL this season that is played on Overwatch 2 with new maps, hero changes and 1 new hero Sojourn peaked at like little under 100k viewers on YouTube. So no I don't think its esport is any threat to Valorant since I don't believe that it will get that massive of a boost and OWL has existed since 2018 and it hasn't killed or badly damaged single esport to my knowledge outside of maybe something like TF2 at start since they lost good amount of talent.
And overall who doesn't own copy of OW already? Also they have free weekends quite often. I really hope OW makes comeback, but I don't think it will damage Valorant (like any established game) at all. It can easily exist in its own space without damaging other and I don't think there's going to be huge surge of people wanting to become OW pros like when OWL was announced originally.