Crash Course in Romance, but I can't really say anymore about it 😉

K2, episode 1, Ji Changwook's character was eating dried squid when a stray cat was around, so he gave the cat some of the dried squid.

Wok of love, Poong (Junho) and Saewoo (Jung Ryeowon) fed a stray cat many times, so I don't remember the exact episodes.

Quenn of tears .... I actually giffed it ....
https://www.dramabeans.com/activity/p/1557713/#acomment-1557715
and also
https://www.dramabeans.com/members/CecilieDK/activity/1558635/

Also "Baby" from currently streaming No Gain No Love
I giffed something, but you might consider it a Spoiler
Not very much, though.
https://www.dramabeans.com/members/CecilieDK/activity/1625293/?nid=5233804&nidwpc=1625293

No Gain No Love (episodes 1-3)
Twinkling Watermelon (episode 13)

Ah, it's frustrating because I know I've seen more but I don't remember any.

I can't say the episodes but some dramas where someone feeds stray cats are:

_ While you were sleeping (Kang Ki Young's character).
_ My Sweet Mobster (Yang Hyun Min's character).

Oh, doesn't she start out by feeding that cat in Miss Night and Day?

(Funny, because "mis" in Danish is a petname for all cats, corresponding to "pussy" but with less (though some) of the non-cat connotation).

FAKE IT TIL YOU MAKE IT: The ML comes over to the FL's house to feed the strays outside. The flirting and the tension while they are feeding the cats are all the feels--such great chemistry by grown ups.

Miss Night and Day: The cat was the best character in the drama (Miss Day was the best human, of course 😅). I loved how soothing her presence was amid all the chaos. I remember how Miss Night (before she was bifurcated into night and day) fed her milk from her palms. Awwww.. I bet the cat was CGI, though.

Sorry if it stirs up bad memories, but Cat Man from Heartbeat. A stray who did not end up bringing the OTP together in a heartwarming way.

I could be wrong about this, but I seem to remember stray cat feeding in The Smile Has Left Your Eyes.

Through the Darkness - Ha Young feeds a stray cat while staking out murderer #2's house.

Marry My Husband - FL was secretly feeding the stray cat at college

Just Between Lovers

Imaginary Cat: Our titular cat Bok-gil was a stray before she was adopted by our ML. Also, both our leads feed alley cats.

Doctor John - I think it was the second male lead who regularly feeds a stray cat.

Gangnam Beauty. I am going to guess Ep 12, 13. How do people even remember the episode number?

The most recent I can remember is Queen of Tears. Baek Hyun Woo found Hong Hae In feeding a stray cat.

First drama that comes straight about feeding stray cat is definitely While you were Sleeping- Suzy looking for her missing piece of chicken and found out KiYong stole each piece from each order.
And the redflag of being a psychopath for feeding the cat just to poison them later 😱.

This drama also marking Kang Ki Yong as one of the great actor, even in smaller role. From hilarious scholar in 7days Queen to psycho in WYWS, great mentor in Attorney WYW, he can nailed it!

The cat becomes almost a symbol of the evolving relationship between Se-hee and Ji-ho in Because This Is My First Life. At one point, Ji-ho—whose only responsibility is to occasionally feed Se-hee’s cat (whom he just calls “Cat,”)—takes it upon herself to give it what she thinks is a proper name. She even goes so far as to get it a nametag. Se-hee gets angry at her presumption. By the end of the show, they’ve become a couple, with “Uri” wearing the nametag.

I think I remember someone feeding a cat in The Frog. I think it was the ML and the friend who occasionally helped look after his place.

A Time Called You. One of the clues that Min Ju and Jun Hee are not the same person is when one feeds stray cats while the other is afraid of them.

Deerling Jae-soo was a secret stay cat feeder. 😂🤣

His suspicious behavior always gave rise to (viewers) speculation but then the cat was finally out if the bag!! 🙃😄

Nobody mentioned Temperature of Love, Ep. 1, so I'll just throw it in there (because I love that drama <3).