`@safe_debug` does not always work well with `LoggingExtras.jl`

I use [LoggingExtras.jl](https://github.com/JuliaLogging/LoggingExtras.jl) for fine-grained logging control. In the following instance, it seems it does not play well with `GPUCompiler.jl`'s [`@safe_debug`](https://github.com/JuliaGPU/GPUCompiler.jl/blob/master/src/utils.jl#L49-L84):

```julia
# julia
# ]activate --temp
# ] add GPUCompiler, LoggingExtras
using GPUCompiler, Logging, LoggingExtras

# Define a custom filter logger
console_logger = Logging.ConsoleLogger(stdout, Logging.Debug) # deliberately set to debug
info_logger = LoggingExtras.EarlyFilteredLogger(log -> log.level >= Logging.Info, console_logger) # here, I filter out anything below Info
global_logger(info_logger)

# in Julia REPL, test some logging levels:
julia> @info "hi"
[ Info: hi

julia> @debug "hi" # no output

julia> GPUCompiler.@safe_debug "hi"
┌ Debug: hi
└ @ Main REPL[50]:1

```

The example above is a bit contrived because I obviously could achieve this using `Logging.ConsoleLogger(stdout)`. In my actual code, I am using `LoggingExtras.TeeLogger` to write to file and stdout simultaneously, e.g.:
```julia
logger = LoggingExtras.TeeLogger((
LoggingExtras.FileLogger("info.log"), # if I comment out this line, then @safe_debug, below, doesn't print
Logging.ConsoleLogger(stdout)
))
global_logger(logger)

julia> GPUCompiler.@safe_debug "hi"
┌ Debug: hi
└ @ Main REPL[74]:1

```

---
Julia Version 1.11.5, GPUCompiler v1.6.1, LoggingExtras v1.1.0

Start with GPUCompiler.jl's src/utils.jl lines 49-84 and reproduce the issue using the LoggingExtras.EarlyFilteredLogger and TeeLogger examples in the report. Compare @safe_debug with Julia's @debug behavior, then verify that debug messages follow the configured logger filtering while preserving the demonstrated logging setup.

Written by the indexing model from the issue text.