What is the expiation for photographing a woman while she is changing her clothes without her knowledge, for lustful purposes, and then deleting the footage? And is it obligatory to inform her and seek her forgiveness?

What you did is a great sin, and this is evidenced by what Muslim narrated from Abu Hurairah (may Allah be pleased with him) that the Prophet (peace and blessings be upon him) said: "Whoever looks into the house of a people without their permission, it becomes lawful for them to gouge out his eye."

You did well by removing the picture, and your regret for what you did is part of your repentance. You must perform sincere repentance that fulfills its conditions: regretting the act, abandoning it immediately, and resolving not to return to it.

You are not required to inform the woman or seek her forgiveness. Imam An-Nawawi stated that repentance from abstract rights of people, such as backbiting, does not necessitate informing the person if they were unaware of it. For the repentant, regret and seeking forgiveness are sufficient.

A Muslim must always be conscious of Allah's watchful eye over all his deeds. Allah Almighty said: "Or do they think that We hear not their secrets and their private counsels? Yes, [We do], and Our messengers are with them, recording." {Az-Zukhruf:80}.