Emotionally intense anime

White Album 2

This is the first one that comes to mind.

Heyyy these are all movies! (In case you didn't want to invest too much time.)
Into the Forest of Fireflies Light
Wolf Children
The Girl Who Leapt Through Time

Shigatsu wa Kimi no Uso

Here's a recent popular example. Makoto Shinkai is also good for this, 5 cm/s is a personal favorite.

I think I have a different mindset than you when it comes to intense emotions in anime
for me (Code Geass, death note, Madoka Magica, Mirai Nikki) would fall into the category

ReLife

DARLING in the FRANXX People really bash on Darling but romance wise its pretty intense

White Album 2

Your Lie in April
These were recommended already but they are really good so I'm putting em here too

Here are a few that I can think of off the top of my head:
Angel Beats
Golden Time
Orange

I also second White Album 2 and Your Lie in April - 2 of my favorites! :)

Blue Spring Ride
5 Centimeters per Second
Violet Evergarden

Others like Golden Time, ReLIFE, Your Lie in April, etc. have been mentioned but those are my recs.

I agree with most posted here. I'm not gonna mention the ones that are already posted here.

Sakurasou no Pet na Kanojo

Plastic Memories

Kimi no Na wa

Kotonoha no Niwa

I would also think of
Ansatsu Kyoushitsu TV
But it is more action and comedy, but it gets later pretty emotional and since u said "like anohana or koe no katachi" this one doesn't really fit it. I still gave it a mention though.

I'm assuming you're looking for something emotionally intense with drama and more on the realistic side based on the two animes you've mentioned. Here are a few recommandations:
Shigatsu wa Kimi no Uso
Ookami Kodomo no Ame to Yuki
Kono Sekai no Katasumi ni

Here are also some personal recommandations (not directly related to your request) which are not emotionally intense as in going to make you cry but instead either have more deep meanings, are psychologically intense or are more of the softer side etc...

Colorful Movie
Kotonoha no Niwa
Byousoku 5 Centimeter
Perfect Blue

Most of what I know has already been recced, so here's another 2
Anthem of the Heart Beautiful Word Beautiful World
Happy Birthday Inochi Kagayaku Toki

I haven't finished this but seems like a melodrama
One Week Friends

I didn't see it on your list: Grave of the Fireflies.
It's a movie though.

March Comes in Like a Lion

Prepeare crumble in the depths of sadness. Also laugh. Because laughing is the medicine for emotional turmoil.

I'm surprised no one has mentioned Haibane Renmei, but watch it.

Haibane Renmei

Hotaru no Haka
Hotarubi no Mori e
Orange
Shigatsu wa Kimi no Uso
White Album 2
Zankyou no Terror

Here's a list of shows that destroyed my emotions the most.
Shiki
Hunter x Hunter 2011
Violet Evergarden
Made in Abyss
DEVILMAN crybaby

White Album 2
Your Lie in April
Angel Beats
Plastic Memories
Wolf Children

Steins Gate (season 1) is a must and Death Note a course