East Asian Buddhism does not use Santideva's Bodhicaryavatara as a rule.
While there was a translation of this into Chinese early on, it never took off.
In the very recent modern period, maybe 20 years or so, some newer translations
often from Tibetan or Sanskrit, have become popular in Taiwan,
but they are still not at all mainstream, and are more like Taiwanese
Tibetan Buddhism books and stuff.
While the four immeasurables are obviously well known in the Far East,
it would probably be more common to recite the name of Guan(shi)yin Bodhisattva,
(Avalokitesvara), and / or the Great Compassion Dharani (Dabei Zhou /
Mahakarunika-dharani), to generate the appropriate great compassion required.
In East Asia, "bodhicitta" was first translated as 道心, which a lot of people
render as "mind of the path" (if they don't know their Chinese translation history),
but the most common is just 菩提心, "bodhi mind", transliterating the "bodhi".
Usually in the compound involving 發(菩提)心 "aspire (bodhi) mind", which
means to have the inspiration to attain anuttara samyak sambodhi,
in order to liberate all sentient beings.
Refer any and all Mahayana literature for sources.