tailfs: clean up naming and package structure

- Restyles tailfs -> tailFS
- Defines interfaces for main TailFS types
- Moves implemenatation of TailFS into tailfsimpl package

Updates tailscale/corp#16827

Signed-off-by: Percy Wegmann <percy@tailscale.com>

tailfs/tailfsimpl/compositefs/stat.go

@@ -0,0 +1,55 @@
+// Copyright (c) Tailscale Inc & AUTHORS
+// SPDX-License-Identifier: BSD-3-Clause
+
+package compositefs
+
+import (
+	"context"
+	"io/fs"
+
+	"tailscale.com/tailfs/tailfsimpl/shared"
+)
+
+// Stat implements webdav.FileSystem.
+func (cfs *CompositeFileSystem) Stat(ctx context.Context, name string) (fs.FileInfo, error) {
+	if shared.IsRoot(name) {
+		// Root is a directory
+		// always use now() as the modified time to bust caches
+		fi := shared.ReadOnlyDirInfo(name, cfs.now())
+		if cfs.statChildren {
+			// update last modified time based on children
+			cfs.childrenMu.Lock()
+			children := cfs.children
+			cfs.childrenMu.Unlock()
+			for i, child := range children {
+				childInfo, err := child.FS.Stat(ctx, "/")
+				if err != nil {
+					return nil, err
+				}
+				if i == 0 || childInfo.ModTime().After(fi.ModTime()) {
+					fi.ModdedTime = childInfo.ModTime()
+				}
+			}
+		}
+		return fi, nil
+	}
+
+	pathInfo, err := cfs.pathInfoFor(name)
+	if err != nil {
+		return nil, err
+	}
+
+	if pathInfo.refersToChild && !cfs.statChildren {
+		// Return a read-only FileInfo for this child.
+		// Always use now() as the modified time to bust caches.
+		return shared.ReadOnlyDirInfo(name, cfs.now()), nil
+	}
+
+	fi, err := pathInfo.child.FS.Stat(ctx, pathInfo.pathOnChild)
+	if err != nil {
+		return nil, err
+	}
+
+	// we use the full name, which is different than what the child sees
+	return shared.RenamedFileInfo(ctx, name, fi), nil
+}