Smaller teams that have, their managers have generally been pretty good!
No, they generally weren’t (at top level), that is the thing.
1999-2001 Valencia made 2 finals under Cuper. Did not have particular success at Inter, did not manage at top level afterwards
2000-2001 Leads under O’Leary made semis. He did nothing of note in his career afterwards
2001-2002 Bayer made CL final under Topmöller. He never even managed, let alone had success on a higher level.
2003-2004 Monaco made final under Deschamps. He had a successful national team career in management but no success at club level afterwards
Porto final under Jose - this one was by a top coach, no question
Deportivo semifinal under Irureta - he did not have success elsewhere
2004-2005 PSV made semis under Hiddink - decent career at national level afterwards, no notable managerial spells except Chelsea interim, so he was kind of on the decline at the time already
2005-2006 Pellegrini made semis with Villarreal, good coach that got top jobs afterwards but hardly a top one
2009-2010 Lyon made Semis under Puel. Did not manage on a higher level after.
2010-2011 Schalke made semis under Magath/Rangnik. Neither have shown themselves to be able to successfully manger a higher level club
2012-2013 Dortmund under Klopp made finals. Top manager no question
2013-2014 & 2015-2016 - Athletico under Simeone - top manager no question
2016-2017 Monaco under Jardim made semis. He is managing in Qatar now.
2017-2018 - Roma made semis under Eusebio di Francesco who is managing mighty Frosione now.
2018-2019 - Ajax with EtH made semis. Poch beat him and made final with Spurs - hardly anyone would want him to manage us now
2019-2020 Leipzig made semis under Nagelsmann who is good, but also Lyon made semis under Rudi Garcia who was managing in Saudi Arabia in a few years
2021-2022 Villareal under Emery made semis, good coach but no particular success at a higher level yet
so plenty of smaller clubs made CL semis over recent decades, most of the managers have gone to do a grand total of nothing at a higher level afterwards. Plus this is ignoring managers who are nowhere near good but made semis/finals/won the whole thing with a bigger clubs like Di Matteo or Grant etc etc. it is a cup competition, this happens.
We can debate on what is a good manager and what is a small club but the big picture is clear I think. Making CL semis with a smaller club is a plus on managers CV but hardly indicative of whether he will come good at higher levels. For every Klopp there are 2-3 jardims, puels and Rudi Garcias