This made me go back through all my stays in my spreadsheet and add what welcome gift if any I've received during my stays since qualifying as Ambassador early Dec 2022. Here are the results and pictures (where I remembered to capture one):

Hotels with welcome gift:
The Ritz-Carlton, Berlin - Bottle of Sparkling Wine (it was my Ambassador qualifying visit, 100th night)
The Ritz-Carlton, Geneva - Philippe Pascoet Chocolate (to die for) & welcome note (received this on multiple stays)
Marriott Geneva - Chocolate & Wine & welcome note (received this on multiple stays)
Marriott Paris Opera Ambassador - Chocolate & Wine & welcome note (in both rooms I booked)
Marriott CDG - Air France "remove before flight tag" & Chocolate & Handwritten welcome note
The Shanghai EDITION - Homemade Chocolate & Fruit Bowl & Handwritten welcome note (received this on multiple stays)
The Westin Beijing Chaoyang - Two bags of nuts & a sparkling water (this wins the most bizarre welcome gift)
Renaissance Beijing Wangfujing Hotel - Bowl of fruit
The Ritz-Carlton, St. Thomas - Bottle of Wine & Handwritten welcome note
Delta BTV - A few snacks & Handwritten welcome note


Hotels that gave nothing:
New York Marriott at the Brooklyn Bridge - Nothing
The New York EDITION - Nothing (received this on multiple stays)
Renaissance New York Chelsea Hotel - Nothing
Beijing Marriott Hotel Northeast - Nothing
The Ritz-Carlton, Half Moon Bay - Nothing
W Hollywood - Nothing (received this on multiple stays)
Newark Liberty International Airport Marriott - Nothing (received this on multiple stays)

Based on my sampling it seems like most domestic hotels give nothing and almost all international do. (shout out to Delta in Burlington, VT for going the extra mile and shame on Beijing Marriott Hotel Northeast, although no welcome note & gift is the least of their problems)

What is most surprising to me is the lack of effort from Domestic Ritz and EDITION properties.