Textra has no full screen or pop-up ads NONE, ZERO, ZILCH.
The problem with Android is that other apps can display windows on top of your apps, thus making it appear like they came from the current app (Textra in this case).
Although not our issue, we are happy to help you locate the offending app (if only to prove this to you and gain your trust back).
Send me a screenshot of Android Settings > Apps > (cog) > Draw over others app (sometimes called 'Apps that can appear on top') you'll see a list of apps that use this Special Permission (that allows a window to be shown on top of Textra, thus tricking you into thinking it's Textra).
OR it's your keyboard app.