Does Using a Private Transaction Relay Guarantee a Transaction Will Be Included in the Next Block?

No, using a private transaction relay does not guarantee inclusion in the next block. The relay service and the block builder/validator it communicates with are incentivized to include the transaction, but they are not obligated to do so.

Inclusion depends on factors like the gas fee offered in the bundle, network congestion, and the builder's own optimization strategy for creating the most profitable block. The transaction might be delayed or fail to be included if a more profitable block can be constructed without it.