Prelate will attempt to autocast Inspire once you get the upgrade for military units, on siege weapons, while tooltip states infantry specifically, I assume that working on Archery and Stables units is intended behavior.
Siege unit Effects:
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Springald: Ability will cast and the Springald will act like it has inspire in regards to casting on it again, but will have no visible changes on performance, stat card, or have the inspire buff icon on its stat overview. Once you have cast inspire on a Springald, it will indefinitely be unable to receive another cast.
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Mangonels + Siege Tower:
The prelate will be stuck attempting to cast inspire on these units over and over to no avail.
Prelate Recasting siege tower - YouTube -
Battering Ram, Trebuchet, Culverin, Bombard:
Will all receive inspire as it would normally work on any intended unit