I did a search on ClinicalTrials.gov using Condition or disease = covid-19 and Other terms = gargle. It returned 40 results, the vast majority of which are taking place outside the US. Of those inside the US, 7 are in 'active recruiting' status, one is 'active' and a whopping 3 have been canceled or withdrawn. The US is the only country showing canceled or withdrawn studies under this search criteria.

A Spanish study showed no statistically significant difference in viral load after use of mouthwash.

I can't find any published discussion of this completed study out of Stanford on the efficacy of povidone-iodine (PVP-I) containing nasal sprays as compared to isotonic saline nasal sprays in COVID-19 positive patients, but the data seems to suggest that they all work to some degree. (See the Analysis Population Description section.)

There's clearly a lot of scientific interest in using mouthwash and nasal sprays consisting of commerically available ingredients, just not much in the US and certainly not in the media.