Unless things have changed in the last 15 years, when I lived there most of my Taiwanese peers used bopomofo aka 注音 as their primary IME for smartphones / laptops / etc.

The few English ex-pats that I knew used the 搜狗 software which defaults to pinyin I think.

I mostly used pinyin on my laptop and bopomofo on my phone (old model that didn't support pinyin) which was mildly annoying. I constantly got it confused with my Japanese since I also read hiragana/katakana and some of the symbols are highly similar.