AlNiCo is very old-fashioned for most uses. Especially, it demagnetizes easily, sometimes just because the magnetic circuit is not closed. But it's less brittle than ceramic and rare earth magnets, and resists corrosion better than rare earth magnets.
Ptfe can withstand +350°C (not 400°C normally) but only if the other constraints are very mild. For instance, its rubbing properties are horrible (abrasion, friction coefficient) above some +50°C already and continue to degrade.
Bare AlNiCo is still available: Bakker Magnetics, Thyssen Krupp... You could buy a part, or turn one to shape and size, and let it cover with electrolytic nickel, cobalt or their alloy, if they are compatible with your reactants and products. Sn can be put over Ni, for instance by dipping the Ni-covered part in liquid Sn. At least, Ni, Co and Sn won't scratch your glass vessels.
Hey, I wrote Ni and Co from my time as a mechanical engineer, but you chemist may prefer to coat them yourself with Ag or Au.
These AlNiCo magnets are meant for electric guitars and their size could match a stirbar:
www.ebay.com/itm/222504778553www.ebay.com/itm/122047741148makes an affordable try.