Custom font in AnkiDroid in Android 9? (Kanji Stroke Order)
Short answer
The problem was in the font file. In case of Kanji Stroke Order, I used version 4.002 while newer version (4.004 when writing this answer), which can be downloaded at www.nihilist.org.uk, is working.
Long answer
I somehow missed faq when custom font is not working on AnkiDroid - it's good idea to check all of them.
My problem would be caught at point #9 (try different font) or #10 (if #9 is working, it means my font is not supported), although I found it already during test #5 - test on both Anki Desktop and Anki Web. As stated in question, I already tried the desktop, but until now I didn't try the web version. Turns out that web version wasn't working, but I could open developer console where I found out that the font file is referenced correctly, but browser has an issue with it.
Moral of the story:

AnkiDroid is using web browser functionality to display cards. Whether something on card (e.g. a font) works depends on the device.
When trying troubleshooting steps, do them all and as exactly as possible. I was really tempted to skip Anki Web (I already proved that my cards and font are working in desktop version) which actually pointed me in the right direction (you can open developer tools in desktop web browser while there is no such thing in AnkiDroid itself).