How do you write a UART receive path that doesn't drop bytes?

Use an interrupt-driven receive feeding a ring buffer, not a polling loop. Configure the RX-not-empty interrupt so the ISR fires the instant a byte arrives; the ISR does the minimum, read the data register (which clears the flag), and enqueue the byte into a ring buffer, then returns, and the main loop dequeues and processes bytes when convenient. This decouples the fast, hard-deadline arrival of bytes from the slower, variable processing in the main loop, which is exactly the single-producer/single-consumer ring-buffer pattern. If you instead poll the RX register in a slow main loop, a byte can arrive and be overwritten by the next one before you read it, the hardware sets an overrun-error flag and you lose data. For very high baud rates where even a per-byte interrupt is too much overhead, you escalate to DMA, which transfers received bytes into a memory buffer with no CPU involvement until a half/full-transfer interrupt. The ring buffer's indices shared with the ISR must be volatile, and you handle the buffer-full case (drop or overwrite) deliberately.