Hi! Welcome to the forum!
So it's not so much that the mouthpiece is inherently bad, it's that it's not historical in design, and makes it harder to achieve the style of playing and articulations of the time. If you're coming to sackbut without any background as a trombone or brass player, another mouthpiece will offer relatively little immediate improvement, as it takes months of playing before you start getting a decent tone and embouchure anyway as a beginner brass player, no matter the mouthpiece. I say that so you don't get your hopes up too much in terms of immediate impact. That being said, it also means getting a more historical mouthpiece won't be as traumatic as it can be to an experienced trombonist used to modern equipment, since you lack the comparison point and you're building your technique from scratch rather than trying to adapt your pre-existing technique. So I would still advise getting one as early as possible. If you start building your technique with a modern mouthpiece, then you're just setting up future obstacles to your learning. Now is the best time to make the switch while you won't yet feel a big difference.
I would recommend a mouthpiece with a flat rim and hemispherical cup with a sharp entrance to the throat, like was typical until the early 19th century. You can go the extra mile and get one that is in several parts with a shank made of rolled sheet brass, like was the norm in the 16th and 17 century, but very few of us use them. Many high level specialists still play one-piece mouthpieces, and some of us use both. The multi-parto, completely historical mouthpieces are generally more expensive as they require more work to make.
The top makers are Geert Jan van der Heide and Egger. Van der Heide's mouthpieces are used by many players, and he can send several by mail for you to try, and you then choose the one you want and send the others back. The drawback is that selling them later on if you switch to something else is not always easy, as they're all unique. I think they go for 200€.
For Egger, see
https://eggerinstruments.ch/en/produkt/ ... outhpiece/. They make really good mouthpieces, and their CNC machining is state-of-the-art and very precise. They are also one of top makers of instruments.
Their range of models is a bit hard to understand. I would recommend the R-series (not the B or K series), and specifically models without a V suffix. RT-6 or RT-5.5 would be a good starting point, and should hold decent resale value because they're quite commonly in demand, and the specs are set and easy to find for potential buyers. Those were 170 Swiss francs in raw brass last time I checked.
Those are one-piece mouthpieces. Both makers also make truly historical multi-part mouthpieces. Egger's is the SO-7 (they made prototypes of larger sized models using the same design/construction but I'm not sure if they're production-ready yet).
