According to BDAG, εὐλάβεια, "the primary meaning relates to exercise of caution; in dealing with the transcendent realm one must be especially cautious about giving offense to deities, hence'reverence, piety', and in our literature, probably only of reverent awe in the presence of God, awe, fear of God"
I note that the word only occurs in Heb 5:7 and Heb 12:28. Modern versions give translations closer to BDAG's meaning such as:
NIV: reverent submission
NLT: deep reverence for God
ESV: reverence
BSB: reverence
BLB: reverent submission
NASB: piety
NKJV: godly fear (I think this is a little misleading)
CSB: reverence
... and so forth. As best I can work out, εὐλάβεια contains no "fear" in the modern sense although that was present originally. However, when deity shows up, one of two things happen. Let me quote two extreme examples:
Isa 25:8, 9, he will swallow up death forever. The Sovereign LORD will wipe away the tears from all faces; he will remove his people's disgrace from all the earth. The LORD has spoken. In that day they will say, "Surely this is our God; we trusted in him, and he saved us. This is the LORD, we trusted in him; let us rejoice and be glad in his salvation." Note that the righteous eagerly look forward to the appearing of the Lord.
Isa 6:14-17, The sky receded like a scroll being rolled up, and every mountain and island was moved from its place.
Rev 6:14-17, Then the kings of the earth, the nobles, the commanders, the rich, the mighty, and every slave and free man, hid in the caves and among the rocks of the mountains. And they said to the mountains and the rocks, “Fall on us and hide us from the face of the One seated on the throne, and from the wrath of the Lamb. For the great day of Their wrath has come, and who is able to withstand it?” The wicked greatly fear the appearance of the Lamb on the Throne.
Thus, the only people who truly fear God are the wicked - the righteous eagerly "long for His appearing" (2 Tim 4:8).
In Heb 5:7, Jesus had no such fear of His Father, but only extreme reverent awe and respect - the perfect example for us.