I don't think that what you are saying shows women as weak. Many people don't use online cab booking services or apps, even in the corporate world. I don't. If I need one I flag down a taxi or my company books me one. That's legitimately something people still do today.
And I don't think there was any plan to stay in Lonavala overnight. If you'll remember, in the episode before Katha said we'll leave early in the morning and be back by the evening. Yes both packed a change of clothes, but people often do that just in case they need one for some reason. Plus she was wearing a full-sleeved shirt and there was no plan to end up spending 2 hours+ outside a dhaba. You can't plan for everything.
I also don't think that in any way were both things to show weakness or the male lead's strength or to show him as a saviour. When he offered to drop Katha home it was because they were late and he didn't think she would get an auto that late. When he did "save" her from those lewd men, he didn't make some heroic gesture in front of her to impress her. He just made it known that he was there and that chased them away. He beat them up later only because they insulted their relationship. And today he offered her the jacket because he himself wasn't wearing it. It's not like he took it off and gave it to her. And she did originally refuse, but accepted when he insisted.
For me, there's nothing wrong with both sequences, nor does it show Katha as weak. And no one is perfect. These small moments show that even in between independence, we all need someone once in a while. If they didn't have these moments then Katha would appear superhuman, which she isn't.
Heck even when she was crying and panicking when Aarav went missing and Viaan helped her along didn't show weakness to me. Any parent in that situation would react like she did and the other would have to step in and be a rock while panicking internally. In a way, that situation perfectly imitated real life. Viaan was panicking as well for Aarav. That's why he stood outside the Gerewal house to ensure that everything was okay and only left when he saw Katha come out with Aarav.