It's a pure mapping problem. There are thousands of known viruses that affect humans. But most viruses don't have thousands of vaccines.
Additionally, there are constraints. The only contraint on a virus is that is needs to reproduce, and cause harm. Any kind of harm will do, and any kind of spreading is fine. But the vaccine needs to not hurt the person (at least, don't hurt them worse than the virus would).
Even if both processes involved similar techniques, the constraints on virus production are more favorable to the researcher than vaccine production.
To get back to whether China or any nation would intentionally create a biological weapon, however...: most industrialized countries realized a long time ago that bioweapons tends to be a bad strategy. Most western countries stopped their bioweapons programs back in the 70s for the simple reason that there was no reasonable use-case for a bioweapon that isn't done better by simply bombing something (or more recently-hacking their infrastructure). Bioweapons are strategically useful for small nations, and terrorist groups.
People underappreciate just how complicated and time-consuming this is.
Immune systems are terrifying things, on trigger alert (they have to be!), and you have to tickle it just right without making everything explode.