Unlike traditional networks such as BTC/ETH, that are using “pending for a long time in the mempool” concept (transactions can sit unconfirmed in a mempool for minutes–hours–days until a miner/validator includes them in a block, or they get dropped), the Sui network is designed so transactions either finalize very quickly or fail/are retried under well-defined conditions. As the maximum execution time for a transaction on the Sui network is under 2 seconds, even for cases where shared-objects are involved, a pending status won’t be the case.
It might be the case that the error "Transaction is rejected as invalid by more than 1/3 of validators" is shown. The following error means that you tried to use the same objects in multiple transactions at the same time. When the same object is used in multiple transactions at the same time, it can result in the object getting locked(stuck) for the remainder of the epoch. It should resolve itself at the end of the current epoch (epochs take 24 hours).