Remove unused search-layer APIs

The following have zero call sites repo-wide:

    SearchManager:🆔 never read or written (also never initialized, nor was it ever used).
    Search::Worker::elapsed_time(): never called. PV output uses tm.elapsed_time() (TimeManager) directly. (removed callers on 25361e5)
    MovePicker::begin()/end(): unused private accessors. (removed callers on 8c2d21f)

closes https://github.com/official-stockfish/Stockfish/pull/6909

No functional change

src/search.cpp

@@ -1836,16 +1836,10 @@ int Search::Worker::reduction(bool i, Depth d, int mn, int delta) const {
 // 'nodestime' option is enabled, it will return the count of nodes searched
 // instead. This function is called to check whether the search should be
 // stopped based on predefined thresholds like time limits or nodes searched.
-//
-// elapsed_time() returns the actual time elapsed since the start of the search.
-// This function is intended for use only when printing PV outputs, and not used
-// for making decisions within the search algorithm itself.
 TimePoint Search::Worker::elapsed() const {
     return main_manager()->tm.elapsed([this]() { return threads.nodes_searched(); });
 }
 
-TimePoint Search::Worker::elapsed_time() const { return main_manager()->tm.elapsed_time(); }
-
 Value Search::Worker::evaluate(const Position& pos) {
     return Eval::evaluate(network[numaAccessToken], pos, accumulatorStack, refreshTable,
                           optimism[pos.side_to_move()]);