Here is a way that will do up to five different sets of numbers that can contain the digits 0-9, comma, and decimal point.

=IFERROR(REGEX.EXTRACT(A2,"[\d,.]+",1),0)+IFERROR(REGEX.EXTRACT(A2,"[\d,.]+",2),0)+IFERROR(REGEX.EXTRACT(A2,"[\d,.]+",3),0)+IFERROR(REGEX.EXTRACT(A2,"[\d,.]+",4),0)+IFERROR(REGEX.EXTRACT(A2,"[\d,.]+",5),0)
If you will have more than 5 numbers, copy one of the pieces of the formula, add it to the end, and increase the number in REGEX.EXTRACT by 1. In other words, follow the same pattern as in the formula above.
REGEX.EXTRACT has the ability to extract an array of all of the numbers but they will be in text form and no SUM function will sum text values so the array cannot be summed. So it was necessary to use the + operator. If someone knows a way to sum the array directly, that would be great.