I also trade BLLB on TD Ameritrade. Schwab has not issued any recent statement announcing changes to trading Caveat Emptor stocks. On December 18th 2020, TD Ameritrade issued notice that they would cease access to trading Caveat Emptor Stocks as of the end of the day on January 31st 2021 and would set them only to sell or hold. It has not yet gone into effect, I would think likely because enacting that policy within the same week of Robinhood and others getting hit with terrible press for doing the same to various individual stocks just didn't seem like the best move from a PR perspective.
There's no reason to mention that fact that certain brokers reflect BLLB as "Pink Sheets Current" as you mentioned because we know that it isn't yet. You can run a quick CTRL + F search on the above link for "BLLB" and see that BLLB would be among those affected specifically because it is not Pink Sheets Current but ideally it will be very soon.
Being that the industry is looking to slowly cease trading on all Caveat Emptor stocks, there are indeed hurdles to trading them and an uplist would certainly be a significant boost to BLLB trading.
The active quotes on BLLB with the OTC were made possible through an interim application approval from OTC Markets after the company requested OTCIQ access in October 2020. I say interim because even prior to potential current listing this allowed them to upload filings in effort to get current. Prior to that approval the OTC Markets would not even show the price of BLLB.