You did not clear it up. William Tyndale used "Easter" for the Jewish passover, not for a claimed pagan festival. The 1535 Coverdale’s Bible has “Easter” at many verses, especially in the Old Testament (Lev. 23:5, Num. 9:2, Josh. 5:10, . . . Ezek. 45:21), which the KJV changed to “passover.“
You do not demonstrate that Luke claims that King Herod was the one who was observing the passover, and you do not demonstrate that Herod would have been observing some pagan festival.
In his commentary on Acts, Paton Gloag asserted that the Herod of Acts 12 “was strict in the observance of the Mosaic law” (I, p. 415). Gloag added: “According to the strict Jews, it was not reckoned lawful to defile their festal days with executions, and Herod Agrippa prided himself on being a strict observer of the law” (I, p. 416). In his commentary on Acts, William Humphrey reported that Josephus maintained that this Herod was “strongly attached to the Jewish law” (p. 100). In his commentary, Livermore maintained that “Herod forbore to execute Peter during the feast of Passover, out of regard to the custom of the Jews” (p. 177). In his 1645 commentary on Acts, John Lightfoot (1602-1675) noted: “Agrippa, having laid hold upon him, deferred his execution till after the Passover” (p. 322). Likewise, the 1645 Westminster Annotations have this note on “the days of unleavened bread” at Acts 12:4: “These words intimate the cause why he deferred Peter’s execution, for reverence of the Passover, which lasted eight days.” In the 1695 second edition of his Paraphrase on the New Testament, Richard Baxter has this note on Acts 12:4: “He set sixteen soldiers to keep him, that after the Passover he might sacrifice him to the people.”
You seem to be ignoring the context at Acts 12:4. The immediate context of Acts 12:4 demonstrated that king Herod was aware that his earlier action of vexing certain of the church “pleased the Jews” (Acts 12:3). The context also revealed that Herod “proceeded further” to take another action that he thought would please the Jews. Would Herod be continuing to please the Jews if he supposedly waited to observe a pagan holiday or festival? Would the celebrations and practices associated with a pagan festival please or offend the Jews? Does the context actually maintain that Herod in proceeding further to take Peter would then do something contradictory to this action intended to please the Jews?
It was actually Luke that used the Greek word pascha for the time for which Herod was waiting since this verse gives no indication that Herod was being directly quoted. The Bible verse or context does not directly say that Herod was keeping or observing pascha. “The people” of Acts 12:4 could be referring to or would be including the Jews mentioned in verse 3. In Acts 12:11, it refers to “the expectation of the people of the Jews.” Therefore according to the context, the Jews were clearly the people that Herod wanted to please again by his further action. Therefore, nothing in the verse and context proves that Herod could not have been waiting for the Jews to finish keeping their pascha so that he could bring Peter forth and please the Jews again. In other words, the context indicates that Herod did not want to risk displeasing the Jews by executing Peter during their Jewish pascha and may not indicate whether Herod personally had any scruples or principles against executing Peter during a festival. Herod also would have no reason to seek to displease the Jews and to honor and respect the church that he was vexing by waiting until after any claimed church celebration. Therefore, the clear evidence from the context clearly supports the understanding that the Jews would be the ones keeping the pascha [also called the feast of unleavened bread in Luke 22:1] instead of the assertion that Herod had to be the one keeping it. If Herod was also keeping it, the context indicates that it was the Jewish pascha that he would be keeping and not some pagan festival nor any Christian celebration.
Moved by the Holy Spirit, Luke could definitely have used the Greek word in the same sense as he did in Luke 22:1. Comparing Scripture with Scripture, the context of Acts 12:3-4 is in agreement with the understanding that this Greek word was used in the same sense as in Luke 22:1.
Perhaps your interpretation of Acts 12:4 would make that verse in the KJV conflict with Luke 22:1 and Ezekiel 45:21.