Your options

RIME?

On ChromeOS normal RIME is not available, however there is a fork of it made for Fyde OS that we can use.

After installing this, you should be able to add FydeOS’s RhythmIME to your active language list.

Note that I take no responsibility for this extension. I didn’t make it.

Configuring

You select layout in the extension options.

Again, it’s all in chinese.

Also, the list of layouts is very restrictive and limited. You can get around it though:

• Download Luna Pinyin and whatever the Zhuyin option was called.
• Edit the schema.yaml fileof luna Pinyin in order to make it Traditional, Traditional (🇹🇼 Standard), Terra Pinyin or Terra Pinyin with 🇹🇼-standard characters, or simplified.