stefan's note is exactly right.
When you start, data represents your data in a named object. As soon as R executes through %>% group_by(...), the values and structure of the object is ephemeral, not existing in a named object. Just like in a <- 5 ; a + 9, the 14 is never assigned to anything. This is often either later explicitly stored into a new object
newdata <- data %>%
  group_by(...) %>%
  summarize(...)
## or less-commonly-seen right-hand assignment
data %>%
  group_by(...) %>%
  summarize(...) -> newdata
or discarded, solely for the side-effect, as you are intending to do here:
data %>%
  group_by(...) %>%
  summarize(...) %>%
  ggplot(...) + geom_point() + ...
In your case, you group and then summarize the data, adding avg_Depression, and then assign data=data referring to the original contents of the object named data. There are two problems with this:
- Your new summarized data is not included here. In fact, - ggplot(.)does not see summarized data, it sees the raw data.
 
- You don't explicitly assign where the piped data is going. Often you may see people code in the - .placeholder for explicit/self-documenting- %>%-pipe-flow, such as
 - mylm <- mydata %>%
  group_by(...) %>%
  summarize(...) %>%
  lm(A ~ B + C, data = .)
 - By default, the - %>%pipe operator will place the data from the previous step (LHS) into the first argument of the next step (RHS). However, if the RHS expression includes the- .placeholder, then the data is assigned to that argument instead. (This does not work the same as the native-R- |>pipe, btw, not a factor here.)
 - Because you do not include the explicit - .placeholder, though, this is what is actually happening:
 -  data %>%
      group_by(Group, Time) %>%
      dplyr::summarise(avg_Depression = mean(Depression),
                      se_Depression = sd(Depression)/sqrt(n())) %>%
      ggplot(., data = data, 
           mapping = aes(...)) + ...
 - which means that the piped data is falling with - ggplot's- ...(catch-all) argument. You don't hear about this because from- ?ggplot2::ggplot:
 -  ```
 Arguments:
     data: Default dataset to use for plot. If not already a data.frame,
           will be converted to one by 'fortify()'. If not specified,
           must be supplied in each layer added to the plot.
  mapping: Default list of aesthetic mappings to use for plot. If not
           specified, must be supplied in each layer added to the plot.
      ...: Other arguments passed on to methods. Not currently used.
 ```
 - the - ...is not currently used.
 
Bottom line, change your data=data to data=. (or just remove data=data completely), and it should work:
 data %>%
      group_by(Group, Time) %>%
      dplyr::summarise(avg_Depression = mean(Depression),
                      se_Depression = sd(Depression)/sqrt(n())) %>%
      ggplot(data = .,                                               # change here 
           mapping = aes(x = Rumination, 
                         y = Depression,
                         color = Time,
                         ymin = avg_Depression - se_Depression,
                         ymax = avg_Depression + se_Depression)) +
                         geom_pointrange(size = 1.2, alpha = .6, 
                         position = position_dodge(width = .1)) +
           geom_smooth(formula = y ~ x, method = lm, se=F)+
           facet_wrap(~Group)+
           theme_bw() +
           theme(panel.grid.major = element_blank(),
                 panel.grid.minor = element_blank())