Yes. You can stay in the US as long as your OPT is pending. Time before your OPT is granted, as shown on your EAD, will not count as days of unemployment. See the OPT policy guidance:
7.1.6. What counts as time unemployed?
Each day (including weekends) during the period when OPT authorization
begins and ends that the student does not have qualifying ...
However, the first statement appears on a site not specific to the a Skilled Worker visa, and could as well mean that some visa types allow a PTE Home test (e.g. spouse visa require only PTE Home A1).
You are correct. The exact requirements differ, both on the level needed and the skills assessed.
PTE Home B1 (cheaper, takes about 30 minutes)
PTE Academic ...