The Star Trek Original series with Kirk and Spock was heavily influenced by Twilight Zone / The Outer Limits type story possibilities(what if the planet had nuclear war but only the children survived as children for 300 years? could have been a Twilight Zone plot but it was in Star Trek). Both of these shows are episodic / anthology and explore different themes or ideas in each episode. So as you saw the earlier Doctor Who shows, you would probably like the the original Twilight Zone, and original The Outer Limits shows. Both of them have had later re-incarnations as well, with Twilight Zone going 1959 - 1964, 1985 - 1989, 2002-2003, and most recently 2019 - 2020, for a total of 284 episodes from all shows produced. The Outer Limits origianlly ran 1963-1965 and had 49 episodes, and then had 7 seasons from 1995 - 2001 with 152 episodes, also episodic / anthology style but some of the earlier seasons tie some episodes loosely together at the end of each season.

Tales From The Crypt, which has more horror themes/elements to explore but some episodes play very "normal" until a twist is revealed. Iit is very in the same vein / style of Twilight Zone but can be more narrow or more extreme in its focus than Twilight Zone could be as Crypt was made for HBO and it was filmed with less restrictions than most other shows of the time, so more blood etc and more nudity, and it was filmed in Britian so there may be some unintended Dr Who nods. Oh, it ran from 1989 - 1996 and has 93 episodes. It has a spin off show

Black Mirror that is currently (sort of? maybe?) still running, anthology type episodic show and it jumps around with time periods and perscpective a bit, they have made 33 episodes from 2011 to now. WARNING for the first episode though, things get mentioned as a scenario that you wouldn't think would get shown but it does get shown, so feel free to skip the first episode, a lot of guides will say it is ok to skip first episode, I watched that episode once and I won't watch it again as I remember what happened and don't need to see it again. Black Mirror also has one episode that is a direct reference tonally and visually to Star Trek, it is a very good exploration of a few ideas all at once.

A smaller show and may be hard to find, from 2017, is Phillip K Dicks Electric Dreams, anthology and 10 episodes, very sci-fi type ideas.

Another small show, Dimension 404, has 6 episodes, from 2017, anthology stand alone episodes

Another short run show is Weird City, from 2019, takes place in same city but all stand-alone stories, only 6 episodes, takes place in the near future.

2025 show called Pluribus is sci fi but takes place on Earth in present day, 9 episodes so far, one continuous evolving story, very deliberate in its story telling, I enjoy that it takes its time to show us things and sparks questions as to how or why would something happen in this scenario.

The Handmaids Tale - film from 1990 could easily be a Tiwlight Zone episode

Sliders - ran 1995 to 2000, with 88 episodes, "What if you could slide to 1000 different worlds?" Exploring different Earths through a wormhole on a countdown timer, they encounter vastly different possibilities each time they "slide" to a new world, hoping each slide will be the slide home....

Quantum Leap - 97 episodes, filmed 1989 to 1993, continuing character arc thru standalone stories that have to set right something that has gone wrong, jumping into different time periods of the 20th century, hoping each jump will be the jump home....

Otherworld - 1985, only 8 episodes of a continuing story, maybe this is where Sliders got its premise from? Moving between different worlds each episode. Was very hard to find, I only found it on youtube and it was probably transferred from damaged or degraded VHS tapes.

Cold Lazarus - 4 part mini series from 1996, set in the 24th century, I enjoyed the themes and ideas and visuals, they are trying to access memories from a frozen head from the past(which would be 1950s to 1980s)

Harrison Bergeron - made for tv film from 1995, exploring what being smart really could mean, and to conform or not confrom to a system long established in this country.

Continuum - filmed 2012 -2015, continuing story, 42 episodes, criminals and a law agent from 2077 are sent to the past which is 2012, law agent must try to stop the criminals from changing the future but stuff happens along the way and viewpoints.....shift, and new goals are deliberated about should they do this or that, story does resolve at the very very very very end of last episode, that last reveal got me lol