Unfortunately your video is difficult to see, but nice effort? Actually, I don't see the BIAB-VST GUI in the picture at all.

Here is what I can tell you about Reaper and BIAB-VST (I have used this combo for the past three years). The BIAB-VST (v1) introduced in Dec 2018 was very prone to failures unless you strongly painted within the lines. Go outside the lines and bad things could happen. BIAB-VST (v2) introduced in Dec 2019 was marginally improved. Many new features were added but still buggy at times, however very functional by final build. By Dec 2020 BIAB-VST v3 finally lived up to the high expectations we all had. I am pleased to say that as of today BIAB-VST v3 (Build 3.4.6) is clicking on all cylinders in Reaper. But I guess that's not much help to you since you are on last years version.

So first confirm you have the final most up to date build for your V2 in BIAB2020. Assuming we are talking about the PC version, that would be DAW Plugin 2.12.15 Update found here: https://www.pgmusic.com/support_windowsupdates.htm . You should be using the .VST3 version of the plugin in Reaper. Keep in mind you can only have one version of the BIAB-VST loaded in a project. And if you have BIAB standalone open you can not share an ASIO driver so set BIAB to MME or WAS.

You may have to deal with some limitations but it should be functional for you. Just for the record, I never remember any specific issue with using time-selection in Reaper and the BIAB-VST. Like I said, current V3 can actually be enjoyable at time. Good Luck.

Dan, BIAB2024, SoundCloud Win11, i7(12thGen), 32GB, 1TB SSD(M.2 NVMe SSD), 2TB Libraries, 1 TB(WD-Black), 2TB SSD(M.2 NVMe SSD)Data, Motu Audio Express, Keystation 61, SL88 Studio, Reaper