Does a device with USB HS Device support necessarily support host mode?
USB High Speed device support necessarily comes with USB (full speed,
at least) Host support

Absolutely NO. &quot;Device support&quot; and &quot;Host support&quot; are two entirely different functions and require different hardware blocks. HS (high-speed 480 Mbps) USB Host support requires probably 10 times more resources than a &quot;HS device&quot;. That's why you rarely find two HS USB controllers, HOST controller, and DEVICE controller in a cheap low-end MCU. Only medium-to-high end MCU can afford HS host support, which also requires significant intelligence on software side and system memory resources. So a MCU with &quot;USB HS Host support&quot; are in totally different class.
The MCUs that have host and device functions (usually multiplexed into the same set of connector pins) are frequently dubbed as &quot;OTG&quot;, a largely meaningles moniker &quot;On-The-Go&quot;. Nowadays it is called &quot;Dual-Role USB port&quot;.