Let's see some details of the law in Numbers 19:11.
Step 1: Sacrifice and burn a heifer:
Numbers 19:1 The Lord said to Moses and Aaron: 2“This is a requirement of the law that the Lord has commanded: Tell the Israelites to bring you a red heifer without defect or blemish and that has never been under a yoke. 3Give it to Eleazar the priest; it is to be taken outside the camp and slaughtered in his presence. 4Then Eleazar the priest is to take some of its blood on his finger and sprinkle it seven times toward the front of the tent of meeting. 5While he watches, the heifer is to be burned—its hide, flesh, blood and intestines. 6The priest is to take some cedar wood, hyssop and scarlet wool and throw them onto the burning heifer. 7After that, the priest must wash his clothes and bathe himself with water. He may then come into the camp, but he will be ceremonially unclean till evening. 8The man who burns it must also wash his clothes and bathe with water, and he too will be unclean till evening.
Step 2: Collect the ashes.
9 “A man who is clean shall gather up the ashes of the heifer and put them in a ceremonially clean place outside the camp.
Step 3: Use it to make the special water of cleansing:
They are to be kept by the Israelite community for use in the water of cleansing; it is for purification from sin. 10The man who gathers up the ashes of the heifer must also wash his clothes, and he too will be unclean till evening. This will be a lasting ordinance both for the Israelites and for the foreigners residing among them.
Step 4: Apply this special water:
11 “Whoever touches a human corpse will be unclean for seven days. 12They must purify themselves with the water on the third day and on the seventh day; then they will be clean. But if they do not purify themselves on the third and seventh days, they will not be clean. 13If they fail to purify themselves after touching a human corpse, they defile the Lord’s tabernacle. They must be cut off from Israel. Because the water of cleansing has not been sprinkled on them, they are unclean; their uncleanness remains on them.
Now let's go back in time to Exodus 13:19
Moses took the bones of Joseph with him because Joseph had made the Israelites swear an oath. He had said, "God will surely come to your aid, and then you must carry my bones up with you from this place."
At this time, the law in Numbers 19:11 had not been established yet. Neither was the tabernacle or the provision for the special water of cleansing.
Based on Numbers 19:11, was Moses unclean during the splitting of יַם־ס֑וּף Yam-Suf?
Moses was not unclean. The law came years later and it was not retroactive.