feat: add C implementation for `blas/base/dsyr` #22316

Job	Run time
Update copyright header years	0s
Print a list of available slash commands	0s
Auto-fix lint errors	0s
Post a comment with make command instructions	0s
Merge changes from develop branch into this PR	0s
Rebase this PR on top of develop branch	0s
Check for required files	0s
Remove in-progress label	0s
Add initial reaction	-7s
	-7s

Provide feedback