The short answer is no.
The long answer is quite complicated and involves many studies which can be found on google scholar. I will go into 2 briefly below in layman terms later.
If we take what happens to the body when actually clinically starving you will see why you are not in starvation mode.
Your body will start to increase lipolysis, or breaking down fat to release fatty acids for energy. You’ll break down protein reserves, usually muscle, for another energy source. Symptoms of all of this can include weakness, apathy, memory lapses, and muscle cramps. As you can see you will still continue to lose weight, at an accelerated rate as your body tries to keep you alive.
Most studies on starvation mode (in an average Joe trying to loose weight sense) put people in 2 categories to compare people that have lost weight and people that haven’t. These categories are “reduced obese” and “control"
Reduced obese will be people that are a certain weight, lets say 70kg, but used to be heavier and recently lost weight. “Control” will be people that have been 70kg for a long time and not categorised as obese.
When comparing the 2 groups Martins et al  found that the difference in resting metabolic rates were minimal between the groups even when the reduced obese groups lost a lot of weight consuming only 800 kcals per day.
Weinsier et al  found that after weight loss had occurred and a weight maintenance period started (slight increase in calories to slow/stop weight loss) there was not a significant difference in how many calories burned per day between reduced obese and control individuals. "Failure to establish energy balance after weight loss gives the misleading impression that weight-reduced persons are energy conservative and predisposed to weight regain.”
There are quite a few new studies from 2019 and 2020 that come to the same conclusion. As long as there is an assessment of calorific intake and a transfer to a maintenance amount of calories after weight loss there will not be a weight increase.
Send me a message if you have any questions about starvation mode, diet or nutrition.