Apparently, Telegram Desktop generates these files during "failed" searches when using the
@gif command. The ones that Telegram generates are easily identified by being named with a series of 18 digits (e.g
532576936841446647.download), usually similar to one another, and always at zero-bytes length.
You can replicate the issue by trying some
@gif searches after removing all files and seeing them being generated again.
They're safe to be removed; watch out not to remove the Safari ones, though, unless you'd like to restart your ongoing downloads.