You have detected differences in the groups and a change in the outcome over time, but neither of these effects is related to the intervention. In a pre-post design the interaction is a test of the intervention because you'd expect the pre intervention scores to be similar (especially in a randomized design) and so the intervention effect should show up in the post scores only. This effect (the group difference on post minus the group difference on pre) is the intervention effect and what is tested by time*intervention.

One puzzle is that the groups differ at pre as well as post which suggests its not a randomized design (or you were unlucky).

Here's a step-by-step guide to interpreting within-subject effects in a two-way MANOVA:

Understand the Design: Make sure you understand the design of your study. In a two-way MANOVA, you have two independent variables (IVs), often referred to as factors. These IVs can be within-subjects factors, between-subjects factors, or a combination of both.

Identify the Within-Subject Factors: Determine which of your factors within-subjects factors are. These are the factors that are varied within the same participants.

Examine the Within-Subject Effects: Within-subject effects in MANOVA assess the interaction between the within-subject factors and the dependent variables (DV). They tell you whether the mean scores on the DVs change significantly across the levels of the within-subject factors.

Interpret the Significance: If the within-subject effects are statistically significant, it indicates that there are differences in the means of the dependent variables across the levels of the within-subject factors. In other words, there is an interaction effect between the within-subject factors and the dependent variables.

Examine Interaction Plots: Interaction plots can help you visualize the interaction effects. These plots show the mean scores on the DVs for each combination of levels of the within-subject factors.

Post hoc Tests (if applicable): If you find significant within-subject effects, you may want to conduct post hoc tests to determine which specific levels of the within-subject factors are significantly different from each other.

Consider Effect Size:In addition to statistical significance, consider the effect size of the within-subject effects. Effect size measures such as eta-squared (η²) or partial eta-squared (η²p) can help you understand the magnitude of the interaction effects.

Interpretation Example:For example, if you're studying the effects of different treatments (within-subject factor) on participants' mood and anxiety levels (dependent variables), a significant within-subject effect would indicate that the treatments have different effects on mood and anxiety. You might further examine this by looking at how mood and anxiety levels change over time or across different treatment conditions.

ANOVA or MANOVA are not suitable to examine if there a significant difference between the same population undergone pre and post test for measuring specific variables.