You can force the Steam Survey Popup to appear on Linux as follows:

1) Entirely shutdown / quit from steam.

2) run: sed -i -e '/\"SurveyDate\"/ s/"[0-9].*"/"'$(date +%Y-%m-%d -d "1 year ago")'"/' ~/.local/share/Steam/config/config.vdf

3) Start steam.

Source: Reddit, Changes: Reddit