My wife and I travelled to France a couple of years ago the last week in August and first week in September. The areas that we visited included Chambord and Chenonceau Chateaus. We walked right in to both, not crowded at all.
Would it be reasonable to assume that Portugal would also be less crowded at this time?
No one can predict crowds.
Assumptions never a plus.
For decades my travels were in November. My career dictated that reality. Retired it still remains my preferred travel month. Have always found the month suits me. Some savings on airfare, accommodations.
Make your decision on what month works best for you.
A couple of years ago would have still been very affected by Covid. Portugal is still in high season until at least late September. October has always been my favorite time to travel. Portugal is much better in terms of crowds the first couple of weeks in October. And, the weather is great that time of year. Rains may start in the later part of the month.
We spent last November travelling through Portugal from Porto south through to Coimbra, Evora, Lagos and finally Lisbon. the weather was perfectly “spring-like” without the rain! The only super rainy day was in Belem at the end of November. Crowds were thin. People told us October was still hectic. Hope this helps!