Tampa at a minimum would get a 2027 2nd rounder (63rd overall) if they let his rights expire. It's probably better for both sides to get something done soon, although Howard wouldn't necessarily be delaying his RFA clock since he'd have to sign a 3 year ELC if he signed now (21 years old) vs. a 2 year ELC if he were to sign August 2026 (22 years old).
The indication seems to be that the 2025 Draft isn't deep, so I wouldn't be shocked if there was a team willing to give up a late first if they thought Howard could contend for an NHL spot soon rather than waiting 3+ years with the pick.
Off the top of my head, here's some prospects who forced trades:
2011: Calgary drafted Tim Erixon with the 23rd pick in 2009 but he declined to sign. He would have re-entered the 2011 Draft where some thought he'd be a top 15 pick. Calgary would have received the 53rd pick as compensation but Erixon steered them to trade him to the Rangers. New York gave up picks #45, #57, and a lesser prospect (Roman Horak) and signed Erixon before the deadline. Maybe not the same exact situation since Erixon risked re-entering the draft whereas Howard would not.
2019: Carolina trades Adam Fox to the Rangers for a 2019 2nd and 2020 3rd. Like Howard, Fox had completed his junior year of college and Carolina had his rights for another year. But since Fox wasn't a first rounder, they risked getting nothing if they let Fox go back for his senior year and then become a free agent.
2022: Minnesota drafted with Jack McBain with a 3rd round pick in 2018. McBain didn't want to sign with Minnesota. Since he wasn't a 1st rounder, Minnesota would have received no compensation if McBain went the August 15th route. They'd trade him to Arizona for a 2022 2nd rounder.
2024: Cutter Gauthier and Rutger McGroarty forced trades by declining to sign. Both got decent returns since the field wasn't limited like the cases with Erixon/Fox.
I'm sure I'm forgetting others (John Marino) but as long as Howard doesn't limit the field, I think Tampa should be able to recoup something close to their original investment (31st pick in 2022).