Can we define an independent series for Invoices such that when we convert a quotation to Invoices, it picks up its own sequence format rather than picking up the sequence format for Quotation?

We do now have the option to define an independent series for both Quotes and Invoices

So while your quotes can follow the series Quotes-1, Quotes-2 etc, you can create a separate series for Invoices like SI-001, SI-002 etc.

Upon conversion, the Invoice auto picks up the series starting from "SI" and adds the next available number to it

You need to enable this option that you can find in "Settings" called "Sequence number setting

Check out the screenshot below to locate this option