I called topTable with the following arguments:

orig <- fit_with_contrasts %>%
      topTable(n=Inf, coef=.contr, adjust.method=NULL)

The documentation says that 'A NULL value will result in the default adjustment method, which is "BH"' (limma 3.17 reference manual). So, I expect that the adj.P.Val is BH-adjusted. In actuality, it is holm/hochberg/hommel-adjusted.

orig <- select(P.Value, adj.P.Val)
> for (m in p.adjust.methods) orig[[m]] <- p.adjust(orig$P.Value, method=m); glimpse(orig)
Rows: 11,736
Columns: 10
$ P.Value    <dbl> 5.285413e-14, 5.358058e-14, 2.123710e-13, 2.471529e-13, 3.7...
$ adj.P.Val  <dbl> 6.202961e-10, 6.287681e-10, 2.491962e-09, 2.899845e-09, 4.4...
$ holm       <dbl> 6.202961e-10, 6.287681e-10, 2.491962e-09, 2.899845e-09, 4.4...
$ hochberg   <dbl> 6.202961e-10, 6.287681e-10, 2.491962e-09, 2.899845e-09, 4.4...
$ hommel     <dbl> 6.202432e-10, 6.287681e-10, 2.491537e-09, 2.899598e-09, 4.4...
$ bonferroni <dbl> 6.202961e-10, 6.288217e-10, 2.492386e-09, 2.900587e-09, 4.4...
$ BH         <dbl> 3.144108e-10, 3.144108e-10, 7.251467e-10, 7.251467e-10, 8.9...
$ BY         <dbl> 3.127657e-09, 3.127657e-09, 7.213523e-09, 7.213523e-09, 8.8...
$ fdr        <dbl> 3.144108e-10, 3.144108e-10, 7.251467e-10, 7.251467e-10, 8.9...
$ none       <dbl> 5.285413e-14, 5.358058e-14, 2.123710e-13, 2.471529e-13, 3.7...

This is probably because the default behavior for p.adjust when method=NULL is also holm/hochberg/hommel, not BH.

> sessionInfo()
R version 4.3.1 (2023-06-16)
Platform: x86_64-conda-linux-gnu (64-bit)
Running under: CentOS Linux 7 (Core)

Matrix products: default
BLAS/LAPACK: /data/behmoaras/home/e0175719/miniconda3/envs/xtlr7/lib/libopenblasp-r0.3.23.so;  LAPACK version 3.11.0

locale:
 [1] LC_CTYPE=en_SG.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_SG.UTF-8        LC_COLLATE=en_SG.UTF-8    
 [5] LC_MONETARY=en_SG.UTF-8    LC_MESSAGES=en_SG.UTF-8   
 [7] LC_PAPER=en_SG.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_SG.UTF-8 LC_IDENTIFICATION=C       

time zone: Asia/Singapore
tzcode source: system (glibc)

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] lubridate_1.9.2 forcats_1.0.0   stringr_1.5.0   dplyr_1.1.2    
 [5] purrr_1.0.2     readr_2.1.4     tidyr_1.3.0     tibble_3.2.1   
 [9] ggplot2_3.4.3   tidyverse_2.0.0

loaded via a namespace (and not attached):
 [1] bit_4.0.5        gtable_0.3.4     compiler_4.3.1   crayon_1.5.2    
 [5] tidyselect_1.2.0 parallel_4.3.1   scales_1.2.1     R6_2.5.1        
 [9] generics_0.1.3   munsell_0.5.0    pillar_1.9.0     tzdb_0.4.0      
[13] rlang_1.1.1      utf8_1.2.3       stringi_1.7.12   bit64_4.0.5     
[17] timechange_0.2.0 cli_3.6.1        withr_2.5.0      magrittr_2.0.3  
[21] grid_4.3.1       vroom_1.6.3      hms_1.1.3        lifecycle_1.0.3 
[25] vctrs_0.6.3      glue_1.6.2       fansi_1.0.4      colorspace_2.1-0
[29] tools_4.3.1      pkgconfig_2.0.3

Yes, you're right, setting adjust.method=NULL for topTable does give Holm's method instead of BH, so the limma documentation is wrong in that respect. And you are also right that the adjust.method=NULL behaviour is determined by p.adjust().

I will fix the behaviour to be as documentated.