You could check what the router sends out using wireshark https://weekly-geekly.github.io/articles/340140/
You only need 802.11r for fast transition to work, k and v are to provide additional information to help clients decide when to roam, they don't speed up the disconnect/reconnect process. For them to work, the client also needs to support these features (usually they do unless the hardware is fairly old). So when a client roams from one AP to another, both APs and the client need to support 802.11r for fast transition to work, and AP settings need to be compatible, e.g. same SSID, encryption/key, mobility domain, PMK etc, it's easier to use OpenWrt default (the example above uses default 802.11r settings)
If 802.11r is enabled, wpa_key_mgmt=WPA-PSK FT-PSK should appear in /var/run/hostapd-phy0.conf, FT-PSK wouldn't appear without 802.11r. Some apps could also show detailed WiFi diagnostic information.
WiFi client getting disconnected when it goes to sleep is not related to roaming, it's more to do with power saving. Most Android devices can be configured to keep WiFi connected in standby.