The reason you feel tanks are dying faster now, explained by math (simply)

Lets say, before S9 the tanks had around 600HP bottom line and the squishies had classic 200HP, This is 1/3 Hp ratio. In s9 200hp heroes got 50 extra health and bottom line tanks got 75HP. This is 1/1.50 Ratio. This is the simple reason.

(More) In an absolute values you, as a tank may start living longer, but the sense in relative values. You start living 1 extra second, but DPS also lives 0.6s longer, instead of 0.3s that you could expect. So for the time needed to deal with DPS's extra health as a tank, your own extra health will end up X2 faster than you used to. Now add relative difference of Accuracy between DPS - Tank and Tank - DPS, Permanent 20% antiheal on you, the fact that tanks had more than 600 effective health so the ratio was even higher, means you can not dive and chase as deep and as long as before, you can not sustain damage as long as before, you can not move as further as before. Yes, this is only one part, but all your game tempo, muscular memory, tactics, etc was based around having 1/3+ HP ratio to enemy DPS, and now it has changed, and those may be a small changes, and not that noticeable, but it can make you feel, something is going wrong. To keep original ratio bottom line tanks should have been getting non less, than 150HP bonus
You Simply benefit from bonus health drastically less, than 250Hp heroes