It's a tough one of assess with Southgate.
He's not great tactically and in the 2 biggest moments he froze and tried to shut up shop when we got the lead, which ultimately lead to our downfall. However, England have had tactically astute managers previously with top talent and they didn't come close to the success (I know we didn't win anything, but going deep in international football for England is a success given our disastrous record previously). There also seemed to be a shift away from that in the World Cup where we took the game to France and were in a position to take the game to extra-time and who knows what happens after that if Kane doesn't miss.
International football requires a slightly different skillset than club football, system managers are often failures in the international game as they don't get the time to work with their players, enrique and flick being the 2 latest examples with poor records internationally at major tournaments. Southgate clearly excels in man management and creating a good environment for an international team to thrive. England no longer have segregated club cliques like the days of the past and everyone seems to actually be in it together. One argument is that footballers are a little softer in this era with regards to rivalry and you can see it at the end of each premier league game when rival players are walking of the pitch embracing, the like would have never been seen in Roy Keane's reign as captain. However, Southgate's influence on this cannot be understated, it was clear in 2018 the atmosphere he was trying to build and it could be seen again when he made an example of sterling back in 2019 when he was a key player for him by dropping him for potentially causing disharmony in the group.
With all that said do I think Southgate is underrated? It depends on the context we're assessing him. I think his skillset has a ceiling in the club game, as 'good vibes' can only get you so far and it soon goes away once the results start to turn. In club football I think he'd be consigned to being the manager who's parachuted in to get the new manager bounce by improving the dressing room culture, but would then be back out the door once the ship had been steadied and clubs want to look for a more expansive type manager. I think his tenure as England manager is criminally underrated though. The team in 2018 was absolute toilet water and we still got to our first semi final in nearly 3 decades. I think we should have won that Euro final, but given where we've come from and the age profile of the squad we have it's still a success and last world cup we were edged out by one of the only teams in the international game who have an equal footing in terms of squad quality. That said I think Southgate's legacy all hinges on the summer, if we win the Euro's, when the dust settles and we inevitably go back to getting knocked out by iceland I think the perception of the success he has had will change significantly. If we don't win it, he will rightly be remembered as the nearly man.