I would like to use the DAVID tool. There were clients in the past but looks outdated.

Could you install and use RDAVIDWebService or DAVIDQuery packages? If I am not wrong these packages are not available for BiocManager::version() 3.13

Are you aware of any R clients interacting with the DAVID (Database for Annotation, Visualization and Integrated Discovery) web service?

DAVIDQuery was removed from Bioconductor back in Bioconductor release 3.4 so likely that is very outdated. Since the RDAVIDWebService package is in ERROR it is likely not working as intended. RDAVIDWebService has yet to build correctly on Bioconductor version 3.13 and therefore not available for download with BiocManager. You could try to download the source code and install manually, but it is not recommended.