Yes! Leviticus 16 does very much foreshadow Matthew 4. In this Matthew instance, it’s the location that provides the connection. The wilderness!
In Marks account we see some additional important information...
MARK 1:12 Immediately the Spirit drove Him into the wilderness.* 13 And He was there in the wilderness forty days, tempted by Satan, and was with the wild beasts; and the angels ministered to Him.
The wilderness was seen as the location for evil entities, spirits. Many see [interpret] the reference to ‘wild beasts’ as literal. And although that’s [obviously] ‘right’, it goes much deeper. In ‘second temple thinking’ it was also an idiom for spiritual entities - and it’s these that tormented Jesus prior to the temptation. That’s why [and suggests ‘how’] the ‘angels’ ministered to him.
MAT 12:43 When an unclean spirit goes out of a man, he goes through dry places, seeking rest, and finds none.
The scapegoat of Leviticus 16, azazel, was sent into the wilderness to be tormented, ravaged, by the ‘wild beasts’. ‘Azazel’ has a deep significance, far ‘deeper’ than the traditional explanation lays out, but I’ll leave that discussion out of this as it’s not required. But, Jesus is clearly ‘typecast’ as our ‘scapegoat’.
Important to note that this incident was a pre cursor, a ‘shadow’ of what is to ‘be’, a pre cursor to events outlined in the apocalyptic books/sections in the Bible. It was identifying, signalling that Jesus is the scapegoat. So the Leviticus 16 ‘picture’, Yom Kippur, has yet to be (fully) fulfilled.
And, importantly to note that this ‘signalling’ was combined with the temptation, that is, the temptation had other (separate) important significance to it.