Can a PTFE coated wire heat up enough to be used as a heating element
Water has good thermal conductivity, so the PTFE won't 'insulate the heat' to any noticeable extent provided the the wire is long enough to spread it out. The wire inside might get a bit hotter, but PTFE can withstand up to 260 °C. With the outside being kept cool by the water the inside should not get anywhere near that temperature.
Vacuum flasks are designed to minimize heat loss, so a small heater can work. In one test a 500 ml Thermos dropped from 90 °C to 75 °C in 8 hours. Water has a specific heat capacity of 4182 J/kg.°C, so 500 ml dropping 15 °C in 8 hours corresponds to an average power loss of ~1.1W. That means anything over 1.1W would be enough to (eventually) heat that Thermos flask to 75-90 °C and keep it there.
A typical mug only holds ~250 ml, but the heat loss is far greater. In this test a vacuum insulated mug took ~65 minutes to drop from 90 °C to 75 °C, but a basic ceramic mug lost the same amount in less than 15 minutes. However as temperature gets closer to ambient the heat loss slows down. At 50 °C the ceramic mug lost ~9 °C in 15 minutes, which corresponds to ~10W in 250 ml.

So your 7.5 W should be enough to keep a vacuum insulated mug with lid warm, but may not be sufficient for a standard mug.