fix(startup): server fails if $NVIM_APPNAME is relative dir #30310

Problem:
If $NVIM_APPNAME is a relative dir path, Nvim fails to start its
primary/default server, and `v:servername` is empty.
Root cause is d34c64e342, but this wasn't
noticed until 96128a5076 started reporting the error more loudly.

Solution:
- `server_address_new`: replace slashes "/" in the appname before using
  it as a servername.
- `vim_mktempdir`: always prefer the system-wide top-level "nvim.user/"
  directory. That isn't intended to be specific to NVIM_APPNAME; rather,
  each *subdirectory* ("nvim.user/xxx") is owned by each Nvim instance.
  Nvim "apps" can be identified by the server socket(s) stored in those
  per-Nvim subdirs.

fix #30256

test/functional/options/defaults_spec.lua

@@ -915,7 +915,7 @@ describe('stdpath()', function()
     assert_alive() -- Check for crash. #8393
   end)
 
-  it('supports $NVIM_APPNAME', function()
+  it('$NVIM_APPNAME', function()
     local appname = 'NVIM_APPNAME_TEST' .. ('_'):rep(106)
     clear({ env = { NVIM_APPNAME = appname, NVIM_LOG_FILE = testlog } })
     eq(appname, fn.fnamemodify(fn.stdpath('config'), ':t'))
@@ -957,6 +957,25 @@ describe('stdpath()', function()
     test_appname('a/b\\c', 0)
   end)
 
+  it('$NVIM_APPNAME relative path', function()
+    local tmpdir = t.tmpname(false)
+    t.mkdir(tmpdir)
+
+    clear({
+      args_rm = { '--listen' },
+      env = {
+        NVIM_APPNAME = 'relative/appname',
+        NVIM_LOG_FILE = testlog,
+        TMPDIR = tmpdir,
+      },
+    })
+
+    t.matches(vim.pesc(tmpdir), fn.tempname():gsub('\\', '/'))
+    t.assert_nolog('tempdir', testlog, 100)
+    t.assert_nolog('TMPDIR', testlog, 100)
+    t.matches([=[[/\\]relative%-appname.[^/\\]+]=], api.nvim_get_vvar('servername'))
+  end)
+
   describe('returns a String', function()
     describe('with "config"', function()
       it('knows XDG_CONFIG_HOME', function()