Perhaps like some (many?) of your students, I come to manga through the anime pipeline. I love anime. I watch anime. I think about anime. I read fan fiction about anime. Most importantly, I talk to students about anime.
[What is anime? Film and television animation. What we read is MANGA and what we watch is ANIME.]
Anime is not LESS valuable than manga--it is simply a different format. For me, anime is still under the umbrella of literacy, especially when watched in SUB (i.e. in the original Japanese with subtitles).
Remember, not all manga have anime adaptations and not all anime are based on a manga series, but there is A LOT OF CROSSOVER. Knowing which anime are currently popular can help you get popular titles circulating in your library--just like knowing which YA titles have a recent Netflix adaptation helps generate excitement for reading.
CREATING SPACES WHERE STUDENTS CAN SAFELY CELEBRATE THEIR INTERESTS IS ESSENTIAL. An Anime Club (either in-person or remote) can help make this happen. ASK YOUR STUDENTS WHAT THEY WANT TO WATCH ~ AND THEN PREVIEW THE EPISODES YOURSELF.
Platforms: Crunchyroll, (Funimation has been purchased by Crunchyroll), Netflix, Hulu
Recommendations for Anime Clubs from my students and I (for middle school audiences): My Hero Academia, Spy x Family, Haikyu!, *Demon Slayer, SK8 Infinity, Toilet Bound Hanako-Kun, Ouran High School Host Club, Your Name (film), Weathering With You (film)
*Demon Slayer IS violent. My middle school clubs skew towards 7th and 8th graders and IMO, Demon Slayer is fine to show. Preview for yourself!