Reshaping large long dataset with numerous out of order responses to wide in R

I have a large dataset that contains participant responses to a number of questionnaires. I'm trying to convert it to wide, but the problem is that not all participants answered all questionnaires, so when converting to wide their responses do not line up. There are also no actual variables for each questionnaire, just an overall questionnaire variable, which denotes which questionnaire and item the participant was responding to, and a separate response variable.

The long dataset looks something like this:

#long dataset 
subject<-c(1,1,1,1,1,1,2,2,2,2,2,2)
questionnaire<-c("Q1_1", "Q1_2", "Q1_3", "Q2_1", "Q2_2", "Q2_3", 
                 "Q2_1", "Q2_2", "Q2_3", "Q3_1", "Q3_2", "Q3_3")
response<-c(1,2,1,4,3,1,2,1,5,3,1,2)
uniqid<-c(1,2,3,4,5,6,7,8,9,10,11,12)

long<-as.data.frame(cbind(subject, questionnaire, response, uniqid))

long
   subject questionnaire response uniqid
1        1          Q1_1        1      1
2        1          Q1_2        2      2
3        1          Q1_3        1      3
4        1          Q2_1        4      4
5        1          Q2_2        3      5
6        1          Q2_3        1      6
7        2          Q2_1        2      7
8        2          Q2_2        1      8
9        2          Q2_3        5      9
10       2          Q3_1        3     10
11       2          Q3_2        1     11
12       2          Q3_3        2     12

Q1 represents the first questionnaire, Q2 the second etc. and the _1, _2 etc. are the items within each questionnaire. What I want the data to look like eventually is:

     subject    Q1_1    Q1_2    Q1_3    Q2_1    Q2_2    Q2_3  
1          1       1       2       1       4       3       1
2          2       NA      NA      NA      2       1       5      

And so on for each questionnaire and item.

The data currently looks more like this:

    subject    questionnaire.1    response.1    questionnaire.2    response.2 
1         1               Q1_1             1               Q1_2             2
2         2               Q2_1             2               Q2_2             1 

etc.

I'm running into 2 problems at the moment.

1. Not all participants answered all questionnaires. They start questionnaires at different times to others. That leads to responses to different questionnaires in the same columns when converting to wide. i.e. as above, participant 1 is answering questionnaire 1 item 1 in the questionnaire.1 column, while participant 2 is answering questionnaire 2 item 1. I don't know how to make it so each column represents the same questionnaire item for all participants.

2. I don't want a separate questionnaire and response column, rather just one questionnaire column (i.e. titled Q1_1 etc), with responses from all participants below. That would be easy enough to achieve on its own, but because each column has a number of responses to different questionnaires, I cannot achieve this without first reordering the columns.

The only solution I have thought of is to insert NA rows for questionnaires that each participant did not answer in the long dataset. i.e. in the example above, inserting 3 NA rows for participant 2 where they did not answer the Q1 items. The dataset is very large however, and I'm sure there are easier ways to achieve what I'm trying to do.

library(dplyr)
library(tidyr)

long |> 
  select(-uniqid) |> 
  pivot_wider(names_from = questionnaire, values_from = response)

# A tibble: 2 × 10
  subject Q1_1  Q1_2  Q1_3  Q2_1  Q2_2  Q2_3  Q3_1  Q3_2  Q3_3 
  <chr>   <chr> <chr> <chr> <chr> <chr> <chr> <chr> <chr> <chr>
1 1       1     2     1     4     3     1     NA    NA    NA   
2 2       NA    NA    NA    2     1     5     3     1     2