feat: add C implementation for `blas/base/dsyr` #22163

Job	Run time
Merge changes from develop branch into this PR	0s
Update copyright header years	0s
Auto-fix lint errors	0s
Rebase this PR on top of develop branch	0s
Check for required files	0s
Print a list of available slash commands	0s
Remove in-progress label	0s
Post a comment with make command instructions	-5s
Add initial reaction	-9s
	-14s

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