Anecdotally, and in my recent experience (in North America), the most common noun and verb is increasingly 'telecommute'. People would know what you mean if you said 'teleworking', but it is not nearly such a common term where I live.
You can see a Google Ngram comparison of the popularity of the various words and phrases.
That said, an NGram comparing 'telecommute' and 'telework' instead of 'telecommuting' and 'teleworking' produces the reverse result.
However, because telecommuting is still a relatively new concept that is only now becoming mainstream, it may well be that there are strong regional differences, and that the language is not yet firmly established.
For what it's worth, the Cambridge dictionary cites 'telework/teleworker' as synonyms of 'telecommute/telecommuting'.
So my answer is that there is probably no firm answer. 'Telework', 'telecommute' or 'remote work' are all fine, and you may want to poll colleagues/coworkers for which word they are more familiar with.