[BRE-943] Harden base image with alpine (#365)

## 🎟️ Tracking


[[BRE-943]](https://bitwarden.atlassian.net/jira/software/projects/BRE/boards/144?jql=assignee%20%3D%20712020%3Aac9853d4-55a2-4808-acad-e7b7914eac07&selectedIssue=BRE-943)

## 📔 Objective

As part of ongoing work to harden Docker images, using "better" method
to update to alpine

## ⏰ Reminders before review

- Contributor guidelines followed
- All formatters and local linters executed and passed
- Written new unit and / or integration tests where applicable
- Protected functional changes with optionality (feature flags)
- Used internationalization (i18n) for all UI strings
- CI builds passed
- Communicated to DevOps any deployment requirements
- Updated any necessary documentation (Confluence, contributing docs) or
informed the documentation
  team

## 🦮 Reviewer guidelines

<!-- Suggested interactions but feel free to use (or not) as you desire!
-->

- 👍 (`:+1:`) or similar for great changes
- 📝 (`:memo:`) or ℹ️ (`:information_source:`) for notes or general info
- ❓ (`:question:`) for questions
- 🤔 (`:thinking:`) or 💭 (`:thought_balloon:`) for more open inquiry
that's not quite a confirmed
  issue and could potentially benefit from discussion
- 🎨 (`:art:`) for suggestions / improvements
- ❌ (`:x:`) or ⚠️ (`:warning:`) for more significant problems or
concerns needing attention
- 🌱 (`:seedling:`) or ♻️ (`:recycle:`) for future improvements or
indications of technical debt
- ⛏ (`:pick:`) for minor or nitpick changes


[BRE-943]:
https://bitwarden.atlassian.net/browse/BRE-943?atlOrigin=eyJpIjoiNWRkNTljNzYxNjVmNDY3MDlhMDU5Y2ZhYzA5YTRkZjUiLCJwIjoiZ2l0aHViLWNvbS1KU1cifQ

Author: AmyLGalles

crates/memory-testing/Dockerfile

@@ -1,13 +1,16 @@
 ###############################################
 #                 Build stage                 #
 ###############################################
-FROM rust:1.85 AS base
+FROM rust:1.85-alpine AS base
 WORKDIR /app
 
 # Make sure the correct rust toolchain is installed only once
 COPY rust-toolchain.toml /app/
 RUN rustup show
 
+# Install build dependencies for Alpine
+RUN apk add --no-cache build-base linux-headers musl-dev libc-dev
+
 # Install cargo-chef, to cache dependency builds
 RUN cargo install cargo-chef --version 0.1.71 --locked
 
@@ -28,12 +31,12 @@ RUN cargo build -p memory-testing --release
 ###############################################
 #                  App stage                  #
 ###############################################
-FROM debian:bookworm-slim
+FROM alpine:3.22
 
 # This specifically needs to run as root to be able to capture core dumps
 USER root
 
-RUN apt-get update && apt-get install -y --no-install-recommends gdb=13.1-3 && apt-get clean && rm -rf /var/lib/apt/lists/*
+RUN apk add --no-cache gdb=15.2-r0
 
 # Copy built project from the build stage and the cases.json file
 COPY --from=build /app/target/release/memory-testing /app/target/release/capture-dumps ./