OK - with Excel 2019 and the craziest formula ever:
=SUM( IF( ISTEXT(( FILTERXML( "<main><sub>" & SUBSTITUTE( C10, ",", "</sub><sub>" ) & "</sub></main>", "//sub" ) )), VALUE( RIGHT( ( FILTERXML( "<main><sub>" & SUBSTITUTE( C10, ",", "</sub><sub>" ) & "</sub></main>", "//sub" ) ), LEN( ( FILTERXML( "<main><sub>" & SUBSTITUTE( C10, ",", "</sub><sub>" ) & "</sub></main>", "//sub" ) ) ) - FIND( "-", ( FILTERXML( "<main><sub>" & SUBSTITUTE( C10, ",", "</sub><sub>" ) & "</sub></main>", "//sub" ) )) ) ) - VALUE(LEFT( ( FILTERXML( "<main><sub>" & SUBSTITUTE( C10, ",", "</sub><sub>" ) & "</sub></main>", "//sub" ) ), FIND( "-", ( FILTERXML( "<main><sub>" & SUBSTITUTE( C10, ",", "</sub><sub>" ) & "</sub></main>", "//sub" ) ) )-1 ) ) + 1, IF( YEAR( ( FILTERXML( "<main><sub>" & SUBSTITUTE( C10, ",", "</sub><sub>" ) & "</sub></main>", "//sub" ) ) ) > 1900, ABS( MONTH(( FILTERXML( "<main><sub>" & SUBSTITUTE( C10, ",", "</sub><sub>" ) & "</sub></main>", "//sub" ) ))-DAY( ( FILTERXML( "<main><sub>" & SUBSTITUTE( C10, ",", "</sub><sub>" ) & "</sub></main>", "//sub" ) ) ) ) +1, 1 ) ) )
Which is an expansion of:
=LET( string, C10,
a, TRANSPOSE( FILTERXML( "<main><sub>" & SUBSTITUTE( C10, ",", "</sub><sub>" ) & "</sub></main>", "//sub" ) ),
SUM( IF( ISTEXT(a), VALUE( RIGHT( a, LEN( a ) - FIND( "-", a) ) ) - VALUE(LEFT( a, FIND( "-", a )-1 ) ) + 1,
IF( YEAR( a ) > 1900, ABS( MONTH(a)-DAY(a ) ) +1, 1 ) ) ) )