First, the BDAG definition, which is singular, for this word, προσκυνέω is:
to express in attitude or gesture one's complete dependence on or submission to a high authority figure, (fall down and) worship, do
obeisance to, prostrate oneself before, do reverence to, welcome
respectfully
The 60 occurrences of this verb in the NT can be classified according to the wording of the stated object:
- worship to "Him" (ie, Jesus), Matt 2:2, 8, 11, 8:2, 9:18, 14:33, 15:25, 28:9, Mark 5:6, 15:19, Luke 24:52, John 9:38, Heb 1:6,
- worship to God, Matt 4:10, Luke 4:8, John 4:21, 23, 24, 1 Cor 14:25, Rev 4:10, 7:11, 11:16, 14:7, 19:4, 19:10, 22:9.
- One servant "begs" him [another servant], Matt 18:26
- Rev 3:9 - those who belong to the synagogue of Satan, who claim to be Jews but are liars instead. I will make them come and bow down at your feet and acknowledge that I have loved you.
- worship "me" (ie, Satan), Matt 4:9, Luke 4:7
- worship demons, Rev 9:20
- worship the Dragon, Rev 13:4
- worship the beast, Rev 13:4, 8, 12, 14:9, 11, 19:20
- worship the image to the beast, Rev 13:15, 16:2, 20:4
- worship to him (an angel), Rev 19:10, 22:8
- images of false gods to worship them, Acts 7:43
- No explicit object but only an implied object or general worship at a temple, etc: Matt 20:20 [Jesus implied], Matt 28:17 [Jesus implied], John 4:20 [God implied], John 4:22, 24 [The Father implied], John 12:20, Acts 8:27, Acts 10:25 [Peter implied], Acts 10:25, 24:11, Heb 11:21 [God implied], Rev 5:14 [God and the Lamb implied], 11:1, 15:4 [God implied].
Let us observe several patterns in this survey.
- the grammatical construction used for "worship to Him/God" (usually the dative) is identical to that used when describing worship to Jesus (again with the dative)
- With the exceptions to be listed below worship to anything other than the Father and Jesus is condemned and unlawful and sinful. This is true of the worship of the beast, the dragon, the image of the beast, Peter, an angel, images of false gods, etc. (See the above list for references.)
The exceptions
The exceptions to the above observations are these (my literal translations):
A: Matt 18:26 - Therefore, having fallen down the servant was "worshipping" to him saying, have patience with me and I will pay all to you. Note that in this case, the purpose of the "worship" is to beg time for paying the debt, not adoration of the servant. Thus, in this instance, it would be better to translate προσκυνέω as "begging on his knees" as most versions correct render it.
B: Rev 3:9 - Behold, I give [those] from the synagogue of Satan, those declaring themselves to be Jews but are not (but they lie) - behold I will cause them to come and "worship" before your feet and that shall know that I loved you. Again, observe that the purpose of this bowing at the feet of the saints is not to give adoration to the saints but to acknowledge that they were correct to worship God and that God loved them. Thus, in this instance, it would be better to translate προσκυνέω as "fall down at your feet" as most versions do. Further, notice that the grammatical construction has no dative; that is we do not have "worship to them" or similar - they simply fall at the feet of the saints to acknowledge something.
CONCLUSION
The grammatical construction in all cases in the NT of worship to God (προσκυνήσει τῷ Θεῷ, etc) and worship to Him/Jesus and thus no difference in translation by context or grammar is warranted.
APPENDIX - Command
Regardless of how we translate the verb προσκυνέω, we are told several times in the NT that whatever it is, we must only do it to God alone, Matt 4:10, Luke 4:8, Acts 10:25, 26, Rev 19:10, 22:8, 9.
Yet, despite this, the NT records numerous cases of people worshipping Jesus (as listed above) as one of the many pieces of evidence of the deity of Christ. This is not the only evidence of this in the NT, we also have Jesus referred to many times by the titles of God in the OT, but this is the subject of another question that I will not enter here.