I believe any coach that is coming to Tottenham Hotspur knows what he is signing up for because he has champions league to play which is a matured game and from what I have seen so far, Tottenham Hotspur haven't been a piece of trash in the champions league I mean they always perform well anytime they found themselves there and I am not expecting them to do less this time rather they should do even more better and I believe this Europa cup they won will also ginger there spirit to work harder and put more effort next season.
After checking Tottenham's Champions League history, i found out that what you said is true because apart from 2016/2017 Champions League season when they were eliminated in the group stage, they go within the round of 16 and above in the rest of their appearance in the Champions League. In 1961/1962 when the Champions League was still called the European Cup, Tottenham Hotspur reached the semi final stage, then in 2010/2011 they reached the quarter finals, in 2017/2018, 2019/2020 and 2022/2023 seasons they reached the round of 16 while in 2018/2019 they reached the finals so this history has shown that they always do well in the Champions League whenever they qualify despite that they haven't won the trophy. This implies that the new manager will be required to continue in same legacy of the club which will require an experienced coach who can perform well in the Champions League games. Hope they find a better replacement for Ange Postecoglou.