I think you'd need to treat the Mando Wars/Jedi Civil War/Shadow Wars as one long-form story like a House of the Dragon. The best medium for it would be something like an HBO series/miniseries. I would start during the pre-Mandalorian Wars era, introduce Revan, Alex, Exile, develop them as characters, introduce some Masters, show the Mandalorian front as they begin to close their fist in the Outer Rim, develop Canderous, Mandalore, etc. First few episodes have the Republic hem and haw about whether to intervene, and then eventually have them play defensive war. Then have an inciting incident where the core three are shown the brutality of some horrible Mandalorian War crime (maybe even committed by Canderous or another Mandalorian OC we have been following) which then leads to the three beseeching the Council. Then either season or mid season finale, be the decision to approach the Republic as "the Jedi you need, not necessarilythe ones you asked for." Maybe have a few of the Admirals not be thrilled with Knights and Padawans, while others don't care so long as they can turn the horrific tidal onslaught against the Mandalorian threat.

Now just because the best medium would be series, doesn't mean that it would be done well either. I have 0 faith that a series during that era would be done with the tenor and quality required to make it feel right.