Just to note that if you do need to buy separate tickets, Belfast-Liverpool is not as expensive of a route as Dublin-Holyhead or Belfast-Cairnryan as a foot passenger. Assuming you're travelling on the morning sailing, it's only £22, and £32 on the evening sailing. There's usually (albeit not currently) a pretty much permanent additional half price promotional offer for the morning sailing.
Also, regarding travel restrictions in the Republic, it is perfectly legal to enter the Republic, and to cross the border, for any reason as of May 10th - and you don't need to quarantine if you're going to Northern Ireland, provided you leave the Republic directly and don't return (unless for the sole purpose of taking a flight/ferry back out of the country) for 14 days. You do need to fill out the passenger locator form and get a private PCR test no more than 3 days before travel, but the testing requirement will likely be waived from July 19th for those holding proof of full vaccination.
There are also no restrictions on returning to GB from the Republic - the fine for non-essential travel abroad only applies to Irish residents; and the UK treat the Republic as part of the UK for the purposes of travel restrictions.