DistributedArrays is not thread-safe

Due to the use of globals such as `DistributedArrays.registry`, currently DistributedArrays is not thread-safe:

```julia
julia> versioninfo()
Julia Version 1.11.6
Commit 9615af0f269 (2025-07-09 12:58 UTC)
Build Info:
Official https://julialang.org/ release
Platform Info:
OS: macOS (arm64-apple-darwin24.0.0)
CPU: 10 × Apple M2 Pro
WORD_SIZE: 64
LLVM: libLLVM-16.0.6 (ORCJIT, apple-m2)
Threads: 6 default, 0 interactive, 3 GC (on 6 virtual cores)
Environment:
JULIA_PKG_USE_CLI_GIT = true
JULIA_PKG_PRESERVE_TIERED_INSTALLED = true

julia> using DistributedArrays

julia> v = [rand(10) for _ in 1:1000];

julia> @sync for vi in v
Threads.@spawn distribute(vi)
end;
ERROR: TaskFailedException

nested task error: TaskFailedException

nested task error: AssertionError: Multiple concurrent writes to Dict detected!
Stacktrace:
[1] _setindex!
@ ./dict.jl:337 [inlined]
[2] setindex!(h::Dict{Any, Nothing}, v0::Nothing, key::Tuple{Int64, Int64})
@ Base ./dict.jl:363
[3] push!
@ ./set.jl:137 [inlined]
[4] DArray{…}(id::Tuple{…}, dims::Tuple{…}, pids::Vector{…}, indices::Vector{…}, cuts::Vector{…}, lp::Vector{…})
@ DistributedArrays ~/.julia/packages/DistributedArrays/SxLCk/src/darray.jl:47
[5] construct_localparts(init::DistributedArrays.var"#73#75"{…}, id::Tuple{…}, dims::Tuple{…}, pids::Vector{…}, idxs::Vector{…}, cuts::Vector{…}; T::Nothing, A::Nothing)
@ DistributedArrays ~/.julia/packages/DistributedArrays/SxLCk/src/darray.jl:126
[6] construct_localparts(init::Function, id::Tuple{…}, dims::Tuple{…}, pids::Vector{…}, idxs::Vector{…}, cuts::Vector{…})
@ DistributedArrays ~/.julia/packages/DistributedArrays/SxLCk/src/darray.jl:117
[7] #invokelatest#2
@ ./essentials.jl:1055 [inlined]
[8] invokelatest
@ ./essentials.jl:1052 [inlined]
[9] #153
@ ~/.julia/juliaup/julia-1.11.6+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/Distributed/src/remotecall.jl:425 [inlined]
[10] run_work_thunk(thunk::Distributed.var"#153#154"{…}, print_error::Bool)
@ Distributed ~/.julia/juliaup/julia-1.11.6+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/Distributed/src/process_messages.jl:70
[11] #remotecall_fetch#158
@ ~/.julia/juliaup/julia-1.11.6+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/Distributed/src/remotecall.jl:450 [inlined]
[12] remotecall_fetch
@ ~/.julia/juliaup/julia-1.11.6+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/Distributed/src/remotecall.jl:449 [inlined]
[13] remotecall_fetch
@ ~/.julia/juliaup/julia-1.11.6+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/Distributed/src/remotecall.jl:492 [inlined]
[14] (::DistributedArrays.var"#1#3"{…})()
@ DistributedArrays ~/.julia/packages/DistributedArrays/SxLCk/src/darray.jl:88
Stacktrace:
[1] #remotecall_fetch#158
@ ~/.julia/juliaup/julia-1.11.6+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/Distributed/src/remotecall.jl:451 [inlined]
[2] remotecall_fetch
@ ~/.julia/juliaup/julia-1.11.6+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/Distributed/src/remotecall.jl:449 [inlined]
[3] remotecall_fetch
@ ~/.julia/juliaup/julia-1.11.6+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/Distributed/src/remotecall.jl:492 [inlined]
[4] (::DistributedArrays.var"#1#3"{…})()
@ DistributedArrays ~/.julia/packages/DistributedArrays/SxLCk/src/darray.jl:88
Stacktrace:
[1] sync_end(c::Channel{Any})
@ Base ./task.jl:466
[2] macro expansion
@ ./task.jl:499 [inlined]
[3] DArray(id::Tuple{…}, init::Function, dims::Tuple{…}, pids::Vector{…}, idxs::Vector{…}, cuts::Vector{…})
@ DistributedArrays ~/.julia/packages/DistributedArrays/SxLCk/src/darray.jl:83
[4] DArray(init::Function, dims::Tuple{Int64}, procs::Vector{Int64}, dist::Vector{Int64})
@ DistributedArrays ~/.julia/packages/DistributedArrays/SxLCk/src/darray.jl:177
[5] distribute(A::Vector{Float64}; procs::Vector{Int64}, dist::Vector{Int64})
@ DistributedArrays ~/.julia/packages/DistributedArrays/SxLCk/src/darray.jl:550
[6] distribute(A::Vector{Float64})
@ DistributedArrays ~/.julia/packages/DistributedArrays/SxLCk/src/darray.jl:540
[7] (::var"#7#8"{Vector{Float64}})()
@ Main ./REPL[6]:2

...and 3 more exceptions.

Stacktrace:
[1] sync_end(c::Channel{Any})
@ Base ./task.jl:466
[2] macro expansion
@ task.jl:499 [inlined]
[3] top-level scope
@ REPL[6]:1
Some type information was truncated. Use `show(err)` to see complete types.
```

AFAICT this could be fixed by using task-local states (`OncePerTask` on Julia >= 1.12).

Start with src/darray.jl, especially the DArray constructor and construct_localparts paths shown in the stack trace, and inspect uses of DistributedArrays.registry. Run the concurrent distribute reproducer from the issue first. Done means concurrent calls no longer trigger the Dict concurrent-write assertion and the relevant behavior is covered by tests.

Written by the indexing model from the issue text.