倾 originally means 'to tip over / pour out' (倾倒 'to pour out', 倾家荡产 'pour out the family fortune') + 力 'strength' = 'pour out all one's strength'. Vivid metaphor: tip the bucket of effort all the way over.
register
Written / formal register; common in marketing copy ('倾力打造', 'crafted with full effort') and corporate announcements. Spoken equivalent: 全力 ('full force').