Packing the court with partisans does, in fact, count as court packing. Here's a helpful article: https://www.rutgers.edu/news/what-court-packing
From the article:
"People often use "court packing" to describe changes to the size of the Supreme Court, but it's better understood as any effort to manipulate the Court's membership for partisan ends. A political party that's engaged in court packing will usually violate norms that govern who is appointed (e.g., only appoint jurists who respect precedent) and how the appointment process works (e.g., no appointments during a presidential election).
"Seen from this perspective, the Barrett appointment is classic court packing. The president nominated a hardline conservative who appears to question major parts of U.S. constitutional law. And the Senate majority changed its procedural rules – invented to deny Merrick Garland a hearing – to ram through the nomination as people were voting."
You siding with the partisan politics of members of a supposedly-neutral court who were put there to make the court partisan, doesn't make it normal.