DBI::dbIsValid does not seem to work with postgres

Expectation:
DBI::dbIsValid(connection) should return false if the connection is closed.

Actual behavior: DBI::dbIsValid(connection) returns true when the connection is closed in this postgres example.

con <- DBI::dbConnect(DatabaseConnector::DatabaseConnectorDriver(),
               dbms = "postgresql",
               server = Sys.getenv("CDM5_POSTGRESQL_SERVER"),
               user = Sys.getenv("CDM5_POSTGRESQL_USER"),
               password = Sys.getenv("CDM5_POSTGRESQL_PASSWORD"))


DBI::dbIsValid(con)
#> TRUE
DBI::dbDisconnect(con)
# this returns true
DBI::dbIsValid(con)
#> TRUE
# even though the connection is closed
DBI::dbListTables(con)
#> Error in rJava::.jcall(conn@jConnection, "Ljava/sql/DatabaseMetaData;",  : 
  org.postgresql.util.PSQLException: This connection has been closed.

I can run this code interactively but when I run it using the reprex package it crashes R on my machine which is why I'm not able to provide an actual reprex.

> sessionInfo()
R version 4.3.1 (2023-06-16)
Platform: aarch64-apple-darwin20 (64-bit)
Running under: macOS Sonoma 14.0

Matrix products: default
BLAS:   /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.11.0

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

time zone: Europe/Amsterdam
tzcode source: internal

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

other attached packages:
[1] shiny_1.7.5             DatabaseConnector_6.3.2 usethis_2.2.2           testthat_3.2.0         

loaded via a namespace (and not attached):
 [1] xfun_0.40         bslib_0.5.1       processx_3.8.2    rJava_1.0-6       gargle_1.5.2     
 [6] callr_3.7.3       vctrs_0.6.5       odbc_1.3.5        tools_4.3.1       ps_1.7.5         
[11] generics_0.1.3    tibble_3.2.1      fansi_1.0.6       RSQLite_2.3.2     blob_1.2.4       
[16] pkgconfig_2.0.3   R.oo_1.25.0       checkmate_2.3.0   dbplyr_2.4.0      assertthat_0.2.1 
[21] lifecycle_1.0.4   R.cache_0.16.0    compiler_4.3.1    brio_1.1.3        bigrquery_1.4.2  
[26] httpuv_1.6.11     sass_0.4.7        htmltools_0.5.6   yaml_2.3.7        jquerylib_0.1.4  
[31] pillar_1.9.0      later_1.3.1       ellipsis_0.3.2    R.utils_2.12.2    cachem_1.0.8     
[36] RPostgres_1.4.6   mime_0.12         styler_1.10.2     tidyselect_1.2.0  digest_0.6.33    
[41] dplyr_1.1.4       duckdb_0.8.1-3    purrr_1.0.2       fastmap_1.1.1     cli_3.6.2        
[46] magrittr_2.0.3    triebeard_0.4.1   utf8_1.2.4        clipr_0.8.0       withr_2.5.2      
[51] promises_1.2.1    backports_1.4.1   bit64_4.0.5       rmarkdown_2.24    httr_1.4.7       
[56] bit_4.0.5         R.methodsS3_1.8.2 hms_1.1.3         memoise_2.0.1     evaluate_0.23    
[61] knitr_1.44        miniUI_0.1.1.1    rlang_1.1.2       urltools_1.7.3    Rcpp_1.0.11      
[66] xtable_1.8-4      glue_1.6.2        DBI_1.2.0         reprex_2.0.2      rstudioapi_0.15.0
[71] jsonlite_1.8.7    R6_2.5.1          fs_1.6.3   

No source file or test is named. Start by reproducing the example with DBI::dbIsValid(), DBI::dbDisconnect(), and DBI::dbListTables() against PostgreSQL, then trace how DatabaseConnector handles the JDBC connection state. Done means dbIsValid(con) returns FALSE after dbDisconnect(con) without causing a crash.