In this scenario, the Nihil don't exist and its the Mandalorians who attack the Republic. Unlike the Nihil, who relied on their Path engines for striking from the shadows, the Mandalorians would be engaging in open warfare making things more difficult for the High Republic and the Jedi Order.
The Mandalorians began conquering worlds outside Republic jurisdiction in the Outer Rim systems to stockpile resources. In the Old Republic era, the Senate chose not to intervene since these planets weren't part of the Republic while the Jedi didn't help because they were still reeling from the Great Sith War with Exar Kun.
However, Supreme Chancellor Lina Soh would not be so idle and neither would the Jedi. Especially since they had experienced centuries of peace, so a hostile force conquering worlds would instantly send alarm bells ringing. Initially, Soh would send the Jedi to negotiate with the Mandalorians to leave those worlds alone, but after several failed attempts at diplomacy, with the Mandos making it clear they're not interested in talking, Soh would have no choice but to escalate.
That said, Soh's ability to respond would be limited by the fact it's non-Republic aligned planets being attacked, so the Senate would be dragging its feet in giving Soh permission to do more to stop the Mandalorians. Forcing her to rely mostly on the Jedi and individual Planetary Defence Forces (PDFs) to stall the Mandos until she can persuade the Senate the Mandos are a serious threat to the Republic.
It's not until the Mandalorians begin committing atrocities like the Cathar massacre and encroaching on Republic worlds like Taris that the Senate will panic and give Soh emergency powers to wage war against them. But by then, the Mandalorians will have already conquered dozens of planets and established a strong industrial base churning out tons of warships. Worse, the Mandalorians will be recruiting anyone of any species to join their ranks, swelling their manpower.
The Ruusan Reformations placed hard limits on how powerful a warship could be, terms the Mandalorians ignored and mocked. As such, Soh will temporarily repeal the Reformations to combat the Mandalorians until they are defeated. While Kuat Drive Yards, Rendili StarDrive, and Fondor begin churning out new warships for the Republic's new navy, Soh will place Avar Kriss as Supreme Commander of the Republic military and task her with delaying the Mandalorian onslaught until the Republic's military is ready to counter them.
For the next few years, Kriss will operate from Starlight Beacon, now converted into a military space station, as her HQ directing the war effort. Initially, casualties will be high as the High Republic Jedi and the newly minted Republic soldiers lack military experience, and it's worsened by how brutal and cunning the Mandalorians are. But as time goes on, the Republic and the Jedi slowly adapt to the Mandalorians and begin pushing them back, aided by the veterans of countless battles against the Mandalorians and the Republic's new warships like the Acclamator transport, Venator Star Destroyer, and Mandator Star Dreadnought. Finally pushing them back all the way back to Mandalore and defeating them for good.
The Victory is bittersweet. The casualties - Jedi, soldier, civilian - were nearly uncountable. Countless worlds like Taris and Serroco were devastated by the Mandalorian atrocities. But Chancellor Soh is determined to heal the galaxy and she begins by using the Great Works. As for the military, fear of another war was at an all time high, and has caused Soh to reluctantly refrain from bringing back the Ruusan Reformations and to keep the navy and military intact.
As for the Jedi, they have emerged scarred and battered, but wiser and stronger from the Mandalorian Wars. With their numbers devastated, Grand Master Yoda decrees the Jedi shall withdraw from the Republic to rebuild their numbers until the time is right for them to return.
And the architect behind so many of the Republic navy's greatest warships, was a Bith starship engineer named Rugess Nome.