In Matt. 8:14-17, Jesus healed Peter's mother-in-law, then he expelled demons and "cured all who fared badly." After reporting these events, Matthew applied Isa. 53:4 to Jesus: "He himself took our sicknesses and carried our diseases" (Matt. 8:17 NWT).
"Surely he hath borne our griefs and carried our sorrows" (Isa. 53:4 KJV).
"But his form was ignoble, and inferior to that of the children of men; [he was] a man in suffering, and acquainted with the bearing of sickness, for his face is turned from [us]: he was dishonoured, and not esteemed. He bears our sins, and is pained for us: yet we accounted him to be in trouble, and in suffering, and in affliction" (Isa. 53:3-4 LXX).
"by his knowledge shall my righteous servant justify many; for he shall bear
their iniquities" (Isa. 53:11 KJV).
According to the Gospel of Matthew, Jesus bore the sicknesses and sorrows of humanity when he cured infirm persons. His bearing their sicknesses did not mean that he literally took their pains upon him; he simply relieved them of their spiritual and physical burdens. I think the same principle can apply to 1 Pet. 2:24.
"The theme of one suffering on behalf of the sins of others is repeated in
Isa. 53:4, 5, 11, 12. Matthew interprets Isa. 53:4 LXX ('He bears our sins
and is pained for us') as referring both to spiritual and physical sickness
(Matt. 8:17), and Peter is adopting a similar line [in 1 Pet. 2:24]. In the
Talmud, Isa. 53:4 is taken to mean that Messiah is "the Leprous One" and the 'Sick One' (b. Sanh. 98b) . . . In the OT, to 'bear iniquity' (Lev. 5:17; Num. 14:34 RSV) means to suffer the penalty of its consequences" (Scott, James. 1 and 2 Peter, Jude, 90).
I might need to correct the reference to James Scott. Someone else might have penned the commentary I quote.