The Link Between the Old and the New Testaments, is it the Cornerstone?

For starters, the question used in the title sounds a bit awkward, one might say. So, we know that a cornerstone is the base or foundation of a corner in a building that joins two walls. The reason why I am bringing it up is because both the Old and the New Testaments mention a cornerstone, but when we read the verses that mention a cornerstone, it does not sound at all like a literal meaning. I will show some verses that mention the word, and maybe you will have to think about it on your own, and decide for yourself on the meaning in the context. First, I want to present Psalm 118:22, it says:

“The stone which the builders rejected is become the chief corner-stone (JPS).”
The previous verse, Psalm 118:21 says:

“I will give thanks unto Thee, for Thou hast answered me, and art become my salvation (JPS).”

The verse that followed verse 22 (23), says:

“This is the LORD'S doing; it is marvelous in our eyes.”

Let’s leave Psalms, and move on to another book, Isaiah. Isaiah 28:16 says:

“Therefore thus saith the Lord GOD: Behold, I lay in Zion for a foundation a stone, a tried stone, a costly corner-stone of sure foundation; he that believeth shall not make haste (JPS).”

Now, the same verse with the preceding and proceeding verses sounds as follows:

“Isaiah 28:15 Because ye have said: 'We have made a covenant with death, and with the nether-world are we at agreement; when the scouring scourge shall pass through, it shall not come unto us; for we have made lies our refuge, and in falsehood have we hid ourselves';
Isaiah 28:16 Therefore thus saith the Lord GOD: Behold, I lay in Zion for a foundation a stone, a tried stone, a costly corner-stone of sure foundation; he that believeth shall not make haste.
Isaiah 28:17 And I will make justice the line, and righteousness the plummet; and the hail shall sweep away the refuge of lies, and the waters shall overflow the hiding-place (JPS).”

Now, when we look at the New Testament, this is what 1 Peter 2:6-7 says:

"For it stands in Scripture: "Behold, I am laying in Zion a stone, a cornerstone chosen and precious, and whoever believes in him will not be put to shame." So the honor is for you who believe, but for those who do not believe, "The stone that the builders rejected has become the cornerstone (ESV)"

Okay, I will not get too involved, and I will leave it up to you to investigate about the cornerstone. I will not provide any further clues, so, enjoy your search!

References:

ESV Bible

JPS Tanakh