We could use base R to do this - get the index of 'Freq' and 'SQR' columns ('i1', 'i2'), then get the max of the 'Freq' columns with pmax for each row, replace the 'SQR' corresponding columns where the value for 'Freq' columns is not max to NA, loop over the rows with apply (MARGIN = 1), remove the NA and paste the 'SQR' words.  Create two new columns in 'df1'
i1 <- startsWith(names(df1), 'Freq')
i2 <- startsWith(names(df1), "SQR")
 
f1 <- function(x) {
        if(all(is.na(x))) {
         NA_character_
        } else paste(na.omit(x), collapse = ",")
}
        
mx <- do.call(pmax, c(df1[i1], na.rm = TRUE))
wrd <- apply(replace(df1[i2], df1[i1] != mx, NA), 1, FUN = f1)
df1[c("MaxFreq", "SQR_word")] <- list(mx, wrd)
-output
> df1
                              GUID SESSION_SKEY SEQNUM parent_uid     SQR_01      SQR_02     SQR_03   SQR_04 SQR_05 SQR_06 SQR_07 SQR_08 Freq1 Freq2 Freq3 Freq4
1 004ce66617739f9705a73dd001dd5ff7     3.84e+13     56 2216028557    volkite    culverin       <NA>     <NA>     NA     NA     NA     NA     3     2    NA    NA
2 004ce66617739f9705a73dd001dd5ff7     3.84e+13    153 2216028557 contemptor dreadnought    volkite     <NA>     NA     NA     NA     NA     3     2     3    NA
3 004ce66617739f9705a73dd001dd5ff7     3.84e+13    217 2216028557       land      raider prometheus     <NA>     NA     NA     NA     NA     9     1     1    NA
4 004ce66617739f9705a73dd001dd5ff7     3.84e+13     12 2216028557 contemptor     pattern    volkite culverin     NA     NA     NA     NA     3     1     3     2
5 05f7cdbb17a0a45e3fcb79bfffc8817c     3.84e+13    250 1297482930       fake      london     genius     <NA>     NA     NA     NA     NA     2     2     2    NA
6 0827fedf17611f9bede0fab001e6dcad     3.84e+13     62   72778457     teapot         for        one      set     NA     NA     NA     NA     1    26     4    21
  Freq5 Freq6 Freq7 Freq8 MaxFreq           SQR_word
1    NA    NA    NA    NA       3            volkite
2    NA    NA    NA    NA       3 contemptor,volkite
3    NA    NA    NA    NA       9               land
4    NA    NA    NA    NA       3 contemptor,volkite
5    NA    NA    NA    NA       2 fake,london,genius
6    NA    NA    NA    NA      26                for
Or may use tidyverse to create the columns - reshape to 'long' format with pivot_longer and do a group by summarise to create the columns and then bind the columns with original data
library(dplyr)
library(tidyr)
library(stringr)
df1 %>% 
   mutate(rn = row_number()) %>% 
   dplyr::select(rn, starts_with("SQR"), starts_with("Freq")) %>% 
   rename_with(~ str_remove(., "_0?")) %>%
   pivot_longer(cols = -rn, names_to = c(".value", "grp"),
       names_sep = "(?<=\\D)(?=\\d)", values_drop_na = TRUE) %>% 
   group_by(rn) %>% 
   summarise(MaxFreq = max(Freq), 
         SQR_word = str_c(SQR[Freq == MaxFreq], collapse=",")) %>% 
   select(-rn) %>%
   bind_cols(df1, .)
-output
                             GUID SESSION_SKEY SEQNUM parent_uid     SQR_01      SQR_02     SQR_03   SQR_04 SQR_05 SQR_06 SQR_07 SQR_08 Freq1 Freq2 Freq3 Freq4
1 004ce66617739f9705a73dd001dd5ff7     3.84e+13     56 2216028557    volkite    culverin       <NA>     <NA>     NA     NA     NA     NA     3     2    NA    NA
2 004ce66617739f9705a73dd001dd5ff7     3.84e+13    153 2216028557 contemptor dreadnought    volkite     <NA>     NA     NA     NA     NA     3     2     3    NA
3 004ce66617739f9705a73dd001dd5ff7     3.84e+13    217 2216028557       land      raider prometheus     <NA>     NA     NA     NA     NA     9     1     1    NA
4 004ce66617739f9705a73dd001dd5ff7     3.84e+13     12 2216028557 contemptor     pattern    volkite culverin     NA     NA     NA     NA     3     1     3     2
5 05f7cdbb17a0a45e3fcb79bfffc8817c     3.84e+13    250 1297482930       fake      london     genius     <NA>     NA     NA     NA     NA     2     2     2    NA
6 0827fedf17611f9bede0fab001e6dcad     3.84e+13     62   72778457     teapot         for        one      set     NA     NA     NA     NA     1    26     4    21
  Freq5 Freq6 Freq7 Freq8 MaxFreq           SQR_word
1    NA    NA    NA    NA       3            volkite
2    NA    NA    NA    NA       3 contemptor,volkite
3    NA    NA    NA    NA       9               land
4    NA    NA    NA    NA       3 contemptor,volkite
5    NA    NA    NA    NA       2 fake,london,genius
6    NA    NA    NA    NA      26                for
data
df1 <- structure(list(GUID = c("004ce66617739f9705a73dd001dd5ff7", "004ce66617739f9705a73dd001dd5ff7", 
"004ce66617739f9705a73dd001dd5ff7", "004ce66617739f9705a73dd001dd5ff7", 
"05f7cdbb17a0a45e3fcb79bfffc8817c", "0827fedf17611f9bede0fab001e6dcad"
), SESSION_SKEY = c(3.84e+13, 3.84e+13, 3.84e+13, 3.84e+13, 3.84e+13, 
3.84e+13), SEQNUM = c(56L, 153L, 217L, 12L, 250L, 62L), parent_uid = c(2216028557, 
2216028557, 2216028557, 2216028557, 1297482930, 72778457), SQR_01 = c("volkite", 
"contemptor", "land", "contemptor", "fake", "teapot"), SQR_02 = c("culverin", 
"dreadnought", "raider", "pattern", "london", "for"), SQR_03 = c(NA, 
"volkite", "prometheus", "volkite", "genius", "one"), SQR_04 = c(NA, 
NA, NA, "culverin", NA, "set"), SQR_05 = c(NA, NA, NA, NA, NA, 
NA), SQR_06 = c(NA, NA, NA, NA, NA, NA), SQR_07 = c(NA, NA, NA, 
NA, NA, NA), SQR_08 = c(NA, NA, NA, NA, NA, NA), Freq1 = c(3L, 
3L, 9L, 3L, 2L, 1L), Freq2 = c(2L, 2L, 1L, 1L, 2L, 26L), Freq3 = c(NA, 
3L, 1L, 3L, 2L, 4L), Freq4 = c(NA, NA, NA, 2L, NA, 21L), Freq5 = c(NA, 
NA, NA, NA, NA, NA), Freq6 = c(NA, NA, NA, NA, NA, NA), Freq7 = c(NA, 
NA, NA, NA, NA, NA), Freq8 = c(NA, NA, NA, NA, NA, NA)), class = "data.frame", row.names = c(NA, 
-6L))