Since the Senate bill addresses new taxes, authorizes spending, as well as spending cuts and spending redirects, can it even be sent to the House directly, since it is a ‘revenue bill” that has to originate in the House?
As a matter of form, it came from the House in the first place. There are two things that augur in favor of the bill being in conformity with the Origination Clause of the constitution. First, that the bill did originate in the House (even though it was basically gutted to a shell and stuffed with Senate language); and second, that unless it is literally a "direct tax" bill, the Supreme Court finds the Constitutional prescription to be unoffended even if the bill is Senate-originated.
See Q126 on Answers From the FAQ, Page 7 - The U.S. Constitution Online for a brief answer, which includes cites to two on-point Supreme Court cases.
US v Munoz-Flores, 495 US 385 (1990)
Twin City v Nebeker, 176 US 196 (1897)
... revenue bills are those that levy taxes, in the strict sense of the word
A set of state law case cites can be found at Origination Clause: Bills to Raise Revenues Must Originate in the House - House Research.