The Templar Brethren were fielded as shock infantry; they're not their own 'faction' yet, they're a specific elite melee unit in the Imperial Fists that represents them.
https://www.forgeworld.co.uk/en-US/Imperial-Fists-Legion-Templar-Brethren-Upgrade-Set are the official models, the Maltese Cross is still there but the tabards and chains aren't.
In general 30k units are much less ornate than
40k units, but there are absolutely outliers, especially in newer units. Templar Brethren aren't sculpted with tabards but Deathwing Companion from the
DA and Crimson Paladins from the
BA are both draped in robes and crusted in logos, so it's not completely out of character for the era if you stick to something closer to the
40k look.
As to fielding a full
TB army I think it'd be perfectly reasonable to run an all black-painted veteran-focused Pride of the Legion-style army with a full motor pool and ranged infantry, and calling it a "Templar Brethren" force. Either they're all literal Templar Brethren from the First Company gathered together in one force with a slightly wider variety of equipment than they normally use when detached to support other companies, or some of them are from another Company that has served alongside the Templar Brethren for a while and been granted the right to wear the black armor as a mark of respect.