How to conduct analysis for experiment data with a mediation model and time series data?

Hi everyone! I am struggling with experiment data analysis as I am not from psychology background.My key research questions are 1. The impact of leader possible self (LPS) (X1) on intention for leadership development (Y1) through the mediation of motivation-to-lead (MTL) (M1), and 2. The role of hope and fear in LPS in impacting that two DVs. All these are measures with scale and I embedded experiment in my online survey for data collection.

At T1, participants got an intervention to write narratives about their future work identity (LPS could be an element related work identity because they are all identities, but the leader / hope / fear elements are not activated). After the narrative writing, they completed the X1, M1 and Y1 measures for me to collect the baseline data

At T2, same participants were randomly assigned to one of the four groups. Group 1 is a control group that they did the same thing as in T1. Group 2 is the LPS hope & fear activation group, that they had to write about their envisioned leader future lives, their hopes and fears. After this, they went on completing the X1, M1 and Y1 measures. Group 3 is LPS hope group (rest of the setup is the same as group 2). Group 4 is LPS fear group (rest of the setup is the same as group 2)

In my previous survey studies, I used EFA and CFA for factor analysis, then went on doing regressions for testing the causal relationships. With the experiment setting, I am confused what the steps should be? It seems to me that I have to conduct one-way ANOVA analysis, my key questions are: what about the factor structure analysis? What about the mediation analysis? By using one-way ANOVA, I can only see the differences between groups. How should I integrate the other steps in the process? What should be a standard process for analysing experiment data actually?
Last edited: